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MSCE Technical Drawing study materials
MSCE Technical Drawing study resources

MSCE Technical Drawing practice questions

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Question 1Drawing instruments, equipment and materials

Which pencil grade is most suitable for drawing firm, dark outlines on a finished technical drawing before inking or reproduction?

  1. 2B Correct answer.
  2. 2H
  3. 9H
  4. HB

Explanation

Softer B-grade graphite deposits more graphite and gives a dark, dense line, which is why 2B or 3B is chosen for final outlines and freehand lettering. Hard pencils like H and 9H are reserved for light construction work because they indent the paper and produce faint lines.

Question 2Drawing instruments, equipment and materials

A drawing sheet is described as A2 in the ISO A-series. What are its nominal dimensions?

  1. 841 mm × 1189 mm
  2. 297 mm × 420 mm
  3. 594 mm × 841 mm Correct answer.
  4. 420 mm × 594 mm

Explanation

The A-series halves each successive size from A0, which measures 841 mm × 1189 mm. A1 is 594 mm × 841 mm, so A2 is the next halving, 420 mm × 594 mm - careful reading of the sequence is needed because the pairs are easily confused.

Question 3Drawing instruments, equipment and materials

What is the standard included angle of the set square that is used to draw lines at 30° and 60° to a reference edge?

  1. 60°–30°
  2. 30°–60° Correct answer.
  3. 90°–45°
  4. 45°

Explanation

The two common set squares are the 45°–45°–90° and the 30°–60°–90° triangles. The 30°–60°–90° square is the one whose acute angles are 30° and 60°, allowing those inclinations to be drawn directly against a T-square.

Question 4Drawing instruments, equipment and materials

Which instrument is designed specifically to draw smooth irregular curves that cannot be produced with a compass?

  1. Divider
  2. Protractor
  3. French curve Correct answer.
  4. Bow compass

Explanation

A French curve (irregular curve) is a template with varying radii along its edge, used to fair in smooth non-circular curves through plotted points. Compasses and dividers handle circles and distances, while a protractor only measures angles.

Question 5Drawing instruments, equipment and materials

What is the main reason a drawing board surface is covered with a smooth, slightly resilient material such as vinyl or basswood rather than bare hardboard?

  1. It gives a softer surface that accepts pencil lines without excessive indentation and allows clean erasure. Correct answer.
  2. It prevents the T-square head from sliding.
  3. It removes the need for a T-square.
  4. It makes the board electrically conductive.

Explanation

A soft, smooth drawing surface lets the pencil glide and keeps hard graphite from scoring the board, and eraser crumbs lift cleanly. The T-square still registers against the board's true edge, so the covering does not replace it.

Question 6Drawing instruments, equipment and materials

A drafter needs to draw a circle of 8 mm radius. Which instrument is most appropriate?

  1. Bow compass Correct answer.
  2. Large bow compass with extension bar
  3. Divider with pen attachment
  4. Beam compass

Explanation

A bow compass is the small-radius instrument, typically covering radii from about 1 mm up to roughly 25 mm with a fine adjustment wheel. Larger radii call for the extension bar or a beam compass, and a divider is for transferring distances rather than drawing circles.

Question 7Drawing instruments, equipment and materials

When sharpening a drawing pencil for technical work, what shape should the graphite point be given?

  1. A long needle point with maximum exposed graphite
  2. A rounded ball point produced by rubbing on paper
  3. A short, well-supported conical point with the graphite slightly blunted Correct answer.
  4. A chisel point formed by sanding one side flat

Explanation

A conical point that exposes a modest amount of graphite and is lightly blunted holds its shape under linework and does not snap or score the sheet. Excessively long needle points break easily and wander off the line.

Question 8Drawing instruments, equipment and materials

How should a T-square be used to draw a horizontal line on a sheet fixed to a drawing board?

  1. Hold the head against the left edge of the board and slide it vertically, drawing along the blade. Correct answer.
  2. Place the blade at an angle to the board edge and rotate it until the line looks level.
  3. Hold the head against the top edge of the board and draw along the blade with the pencil tilted.
  4. Hold the head against the left edge and slide it vertically, but draw only right-to-left.

Explanation

The T-square head is registered against the true working edge (usually the left edge) and slid up or down so the blade stays parallel to the top edge. Lines are then drawn along the blade, giving a family of parallel horizontals; direction of stroke does not change the geometry.

Question 9Drawing instruments, equipment and materials

A drawing must be reproduced photographically and then microfilmed. Which linework practice best preserves legibility through that process?

  1. Draw all lines at the same medium weight.
  2. Use dense, uniform-width lines with strong contrast between thick and thin. Correct answer.
  3. Use the thinnest possible lines to save graphite.
  4. Vary line width randomly to suggest depth.

Explanation

Reproduction and microfilming lose faint or uneven lines, so drawings are made with dense graphite or ink and a clear hierarchy of thick and thin line weights. Uniform medium weight or random variation reduces the contrast that the camera and film rely on.

Question 10Drawing instruments, equipment and materials

Which statement correctly distinguishes a divider from a compass?

  1. A divider draws circles; a compass measures distances.
  2. A divider has two steel points for transferring measurements; a compass has one point and one lead or pen. Correct answer.
  3. A divider is used only with ink; a compass is used only with graphite.
  4. A divider has a pencil lead in each leg; a compass has a single needle point.

Explanation

Both instruments share a hinged joint, but the divider carries two hardened points so it can step off and transfer distances, whereas the compass replaces one point with a lead or pen to sweep arcs and circles. The roles are not interchangeable without swapping attachments.

Question 11Drawing instruments, equipment and materials

What is the purpose of the small knurled centre wheel on a bow compass?

  1. It locks the needle point into the paper.
  2. It stores spare leads.
  3. It holds the pencil at a fixed 45° angle.
  4. It provides fine adjustment of the radius after the legs are set approximately. Correct answer.

Explanation

The centre wheel turns a threaded shaft that opens or closes the legs by small increments, so a radius can be set precisely after rough positioning by hand. It does not anchor the needle or store leads, and the lead angle is set by the user.

Question 12Drawing instruments, equipment and materials

A student's compass keeps slipping because the needle point barely penetrates the sheet. Which adjustment is most appropriate?

  1. Loosen the centre wheel completely.
  2. Shorten the needle so it cannot reach the paper.
  3. Replace the lead with a harder grade.
  4. Lengthen the needle point so it seats firmly in the sheet while the lead still touches. Correct answer.

Explanation

The needle should extend slightly beyond the lead so it beds into the paper and acts as a stable pivot while the lead just contacts the surface. A short needle skates, and changing lead hardness or loosening the wheel does not address the pivot problem.

Question 13Drawing instruments, equipment and materials

In a set of drawing instruments, what is the function of a lengthening bar (extension bar)?

  1. It joins two set squares to form a larger triangle.
  2. It extends the pencil beyond the point for shading.
  3. It extends a compass leg so radii larger than the standard reach can be drawn. Correct answer.
  4. It lengthens the T-square blade for wide sheets.

Explanation

The extension bar is inserted between the compass leg and the lead or pen holder, increasing the effective leg length so circles of larger radius can be swept without switching to a beam compass. It is a compass accessory and has nothing to do with set squares or T-squares.

Question 14Drawing instruments, equipment and materials

A drafter must draw a family of parallel vertical lines spaced exactly 12 mm apart across a sheet. Which combination of equipment gives the most consistent result?

  1. Protractor and freehand pencil strokes
  2. Divider used alone without any straightedge
  3. T-square with the head on the left edge, plus a set square slid along the blade Correct answer.
  4. Scale rule and French curve

Explanation

Vertical lines parallel to the board's side edge are drawn by resting a set square on the T-square blade and sliding it along; the T-square guarantees the reference is square to the board. The scale rule transfers the 12 mm spacing along the blade, but a French curve, protractor or bare divider cannot guarantee straightness and parallelism.

Question 15Drawing instruments, equipment and materials

Why is dusting the drawing surface with a soft brush or cloth preferred over blowing eraser crumbs away by mouth?

  1. Blowing is slower than brushing.
  2. Moisture and oils from breath can mark or warp the sheet and graphite dust may settle unevenly. Correct answer.
  3. Brushes magnetise the graphite.
  4. Eraser crumbs are electrically charged and must be neutralised.

Explanation

Breath carries moisture and oils that can stain or cockle the paper, and it scatters fine graphite unpredictably across the sheet. A soft brush lifts debris away in a controlled direction and protects the surface for redrawing.

Question 16Drawing instruments, equipment and materials

A drawing is to be inked with a ruling pen. Which practice gives a clean, even line?

  1. Hold the pen at 30° to the paper and press hard.
  2. Load the pen and draw slowly so the ink soaks into the sheet.
  3. Set the blades to the required width, fill between them sparingly, and draw steadily with the pen held perpendicular to the line. Correct answer.
  4. Fill the pen generously so the blade floods the line.

Explanation

A ruling pen lays a line whose width equals the gap between the blades, so the gap is set first and only a small charge of ink is carried between the blades. Holding the pen perpendicular to the line and moving steadily keeps the ink flowing evenly without blots or flooding.

Question 17Geometrical construction and plane geometry

A line segment is bisected using a compass and straightedge. Which construction step is essential to produce the perpendicular bisector?

  1. Draw a line through one endpoint at 45 degrees to the segment
  2. Draw a single arc from the midpoint of the segment with radius equal to half the segment
  3. Measure the segment with a scale and mark the midpoint by calculation only
  4. Draw arcs of equal radius from each endpoint that intersect above and below the segment Correct answer.

Explanation

The perpendicular bisector is constructed by striking equal-radius arcs centred on each endpoint so that they intersect on both sides of the segment; the line joining the two intersections is the bisector. Because the arcs have equal radii, every intersection point is equidistant from the two endpoints.

Question 18Geometrical construction and plane geometry

An angle of 60 degrees is constructed with compass and straightedge. Which procedure produces it directly?

  1. Step off four equal chords around a circle and join alternate points
  2. Construct a perpendicular at the vertex and then bisect the resulting angle
  3. Bisect a right angle twice in succession
  4. Construct an equilateral triangle on one arm and use the angle at the vertex Correct answer.

Explanation

An equilateral triangle has all interior angles equal to 60 degrees, so constructing one on a given arm yields a 60-degree angle at the vertex. The construction uses only equal compass arcs, making it a classic straightedge-and-compass result.

Question 19Geometrical construction and plane geometry

Which construction divides a given straight line into any number of equal parts using only parallel lines?

  1. Draw a circle with the line as diameter and divide the circle into equal sectors
  2. Construct the perpendicular bisector at every measured interval along the line
  3. Bisect the line repeatedly until the required number of parts is reached
  4. Draw an inclined line from one end, step off equal divisions along it, then draw parallels to the far end Correct answer.

Explanation

The standard method draws an auxiliary inclined line, marks off the required number of equal steps along it, joins the last mark to the far end of the given line, and draws parallels through the other marks. Parallel projection then divides the original line into equal parts.

Question 20Geometrical construction and plane geometry

A regular hexagon is constructed on a given circle. What is the compass setting used to step around the circumference?

  1. The radius of the circle Correct answer.
  2. The diameter of the circle
  3. Half the radius of the circle
  4. The side of an inscribed square

Explanation

For a regular hexagon the side length equals the circumradius, so stepping the compass around the circle at a radius equal to the circle radius marks the six vertices. This is why the hexagon is one of the easiest regular polygons to construct.

Question 21Geometrical construction and plane geometry

Which pair of instruments is sufficient to construct an angle of 45 degrees from a given straight line at a point on it?

  1. Compass and straightedge Correct answer.
  2. Scale and French curve
  3. Dividers and T-square only
  4. Protractor and set square only

Explanation

A 45-degree angle is obtained by erecting a perpendicular at the point and bisecting the resulting right angle, a construction requiring only a compass and straightedge. No measurement in degrees is needed.

Question 22Geometrical construction and plane geometry

A tangent is drawn to a circle from an external point by constructing a semicircle on the line joining the point to the centre. Why does this work?

  1. The chord of the semicircle equals the radius of the given circle
  2. The arc of the semicircle is parallel to the required tangent
  3. The semicircle divides the external line into two equal parts
  4. The angle in a semicircle is a right angle, so the intersection gives the tangent point Correct answer.

Explanation

The point of tangency lies where the radius meets the tangent at 90 degrees. Since the angle subtended by a diameter at the circumference is a right angle, the intersection of the semicircle with the given circle marks the tangent point.

Question 23Geometrical construction and plane geometry

A regular pentagon is inscribed in a circle. Which construction sequence is correct?

  1. Step the radius around the circle six times
  2. Bisect the diameter twice to obtain the pentagon side
  3. Construct an equilateral triangle on the diameter and use its altitude
  4. Construct two perpendicular diameters, bisect one radius, then strike an arc to locate the pentagon side Correct answer.

Explanation

The conventional pentagon construction uses two perpendicular diameters, bisects one radius, and strikes an arc from that midpoint to set off the side length on the circumference. The resulting chord is then stepped around the circle.

Question 24Geometrical construction and plane geometry

Two circles of radii 30 mm and 20 mm have centres 60 mm apart. What is the nature of their intersection?

  1. They are internally tangent
  2. They are externally tangent
  3. They do not intersect
  4. They intersect at two points Correct answer.

Explanation

The sum of the radii is 50 mm, which is less than the 60 mm centre distance, and the difference is 10 mm, which is less than 60 mm. Because the centre distance lies between the sum and the difference of the radii, the circles cut at two points.

Question 25Geometrical construction and plane geometry

In an ellipse constructed by the concentric-circle method, which pair of circles is drawn first?

  1. Circles with diameters equal to the major axis and half the minor axis
  2. Circles with diameters equal to the major and minor axes Correct answer.
  3. Two circles of equal diameter offset by the focal distance
  4. Circles centred on each focus with radius equal to half the major axis

Explanation

The concentric-circle method begins with two concentric circles whose diameters are the major and minor axes. Radial lines divide both circles, and verticals and horizontals through corresponding points intersect to give points on the ellipse.

Question 26Geometrical construction and plane geometry

An involute of a circle is to be drawn. What is the defining property of this curve?

  1. It is the path of a point on a circle rolling along a straight line
  2. It is the locus of points equidistant from a fixed point and a fixed line
  3. It is the curve whose distance from two fixed points is constant
  4. It is the path traced by a point on a taut string unwound from the circle Correct answer.

Explanation

The involute is traced by the end of a taut string as it unwinds from the circle, so each point lies on a tangent and the string length equals the arc already unwound. This property is used in gear tooth profiles.

Question 27Geometrical construction and plane geometry

A line is to be divided in the ratio 3:5 geometrically. Which method is appropriate?

  1. Bisect the line and then bisect one half
  2. Draw an inclined line with eight equal steps and draw a parallel through the third step Correct answer.
  3. Construct a 60-degree angle at each end and join the intersections
  4. Measure three-fifths of the line with a scale and mark it

Explanation

Ratio division uses an auxiliary inclined line marked into 3 plus 5 equal steps; joining the eighth step to the far end and drawing a parallel through the third step divides the line in the ratio 3:5. The construction relies on similar triangles.

Question 28Geometrical construction and plane geometry

A circle of radius 25 mm is to be divided into twelve equal parts. What chord length is stepped around the circumference?

  1. About 17.7 mm
  2. About 12.9 mm Correct answer.
  3. About 39.3 mm
  4. About 25 mm

Explanation

The chord for a regular twelve-sided division is 2R sin(180/12) = 2 x 25 x sin 15 degrees, which is about 12.9 mm. Stepping this chord twelve times returns to the starting point.

Question 29Geometrical construction and plane geometry

When constructing a parabola given its focus and directrix, each point on the curve satisfies which condition?

  1. Its distance to the focus plus its distance to the directrix is constant
  2. Its distance to the focus equals twice its distance to the directrix
  3. Its distance to the focus equals its perpendicular distance to the directrix Correct answer.
  4. Its distance to the focus is always less than its distance to the directrix

Explanation

The parabola is the locus of points equidistant from the focus and the directrix. Constructing arcs centred on the focus with radii equal to measured directrix distances locates successive points.

Question 30Geometrical construction and plane geometry

Which statement about the bisection of a straight line and the bisection of an angle is correct?

  1. Both constructions rely on intersecting equal-radius arcs Correct answer.
  2. Angle bisection produces a line parallel to one arm
  3. Line bisection needs a scale while angle bisection does not
  4. Both constructions require a protractor to verify the result

Explanation

Both procedures are pure straightedge-and-compass constructions that use intersecting arcs of equal radius to locate points equidistant from the references. This is why they are treated together in plane geometry construction.

Question 31Geometrical construction and plane geometry

A regular octagon is inscribed in a circle. Which construction gives the octagon side directly?

  1. Construct a hexagon and bisect each side
  2. Bisect the diameter into eight equal parts
  3. Bisect the arcs between the vertices of an inscribed square Correct answer.
  4. Step the radius around the circle eight times

Explanation

An inscribed square gives four vertices at 90-degree intervals; bisecting each arc between adjacent vertices adds four more points at 45-degree intervals, producing a regular octagon. The side is the chord subtending 45 degrees.

Question 32Geometrical construction and plane geometry

In the construction of a hypocycloid, a small circle rolls inside a larger fixed circle. What is the resulting curve when the rolling circle diameter equals the radius of the fixed circle?

  1. An ellipse with axes in the ratio 2:1
  2. A parabola opening along the diameter
  3. A circle concentric with the fixed circle
  4. A straight line diameter of the fixed circle Correct answer.

Explanation

When the rolling circle diameter equals the fixed circle radius, the traced point oscillates along a straight line through the centre, a special case of the hypocycloid. This degenerate case is a useful check on the general construction.

Question 33Geometrical construction and plane geometry

An arc of radius R is to be drawn tangent to two straight lines that meet at an angle. How is the centre located?

  1. At the intersection of the two given lines
  2. At the intersection of lines drawn parallel to each given line at distance R Correct answer.
  3. At the midpoint of the chord joining the tangent points
  4. On the angle bisector at distance R from the vertex

Explanation

The centre of a circle tangent to a line lies on a line parallel to it at a distance equal to the radius. Intersecting the two offset parallels therefore locates the centre of the tangent arc.

Question 34Geometrical construction and plane geometry

A line is drawn tangent to a circle at a point on its circumference. What is the relationship between the tangent and the radius at that point?

  1. The tangent is parallel to the radius
  2. The tangent coincides with the diameter through the point
  3. The tangent is perpendicular to the radius Correct answer.
  4. The tangent makes an angle of 45 degrees with the radius

Explanation

A tangent touches the circle at exactly one point, and the radius to that point is perpendicular to the tangent. This right-angle relationship underpins most tangent constructions.

Question 35Geometrical construction and plane geometry

Which construction produces an angle of 30 degrees from a given line at a point on it?

  1. Construct 45 degrees and bisect it
  2. Construct 60 degrees and bisect it Correct answer.
  3. Bisect a straight angle twice
  4. Erect a perpendicular and add a 60-degree angle

Explanation

Bisecting a constructed 60-degree angle gives 30 degrees exactly. The 60-degree angle itself comes from an equilateral triangle construction, so the whole process uses only compass and straightedge.

Question 36Geometrical construction and plane geometry

A circle is to be drawn through three given non-collinear points. Where is its centre?

  1. At the intersection of the perpendicular bisectors of two chords joining the points Correct answer.
  2. At the centroid of the triangle formed by the three points
  3. At the intersection of the angle bisectors of the triangle
  4. At the midpoint of the longest side of the triangle

Explanation

The centre of a circle through three points is equidistant from all of them, so it lies on the perpendicular bisector of every chord between pairs of points. Intersecting two such bisectors gives the circumcentre.

Question 37Geometrical construction and plane geometry

A rectangle is to be constructed with sides in the ratio of the golden section. Which ratio applies?

  1. About 1.618 to 1 Correct answer.
  2. About 2 to 1
  3. About 1.732 to 1
  4. About 1.414 to 1

Explanation

The golden section divides a line so that the whole is to the greater part as the greater part is to the lesser, a ratio of about 1.618 to 1. It is constructed by bisecting one side of a square and striking an arc from that midpoint.

Question 38Geometrical construction and plane geometry

In constructing a normal and tangent to an ellipse at a given point, which property is used?

  1. The normal passes through the centre of the ellipse
  2. The tangent bisects the angle between the focal distances
  3. The normal bisects the angle between the focal distances at that point Correct answer.
  4. The tangent is parallel to the major axis at every point

Explanation

For an ellipse, the normal at a point bisects the angle between the lines joining that point to the two foci. Drawing the bisector of the focal angle therefore gives the normal, and the tangent is drawn perpendicular to it.

Question 39Geometrical construction and plane geometry

A helix is generated on a cylinder. Which pair of parameters fully defines its form?

  1. Diameter of the cylinder and the lead of the helix Correct answer.
  2. Radius of the cylinder and the colour of the line
  3. Diameter of the cylinder and the thickness of the drawing line
  4. Length of the cylinder and the number of visible turns only

Explanation

A helix is defined by the cylinder on which it lies and its lead, the axial advance per full turn. These two parameters fix the pitch angle and the shape of the developed curve.

Question 40Geometrical construction and plane geometry

Two circles of radii 40 mm and 15 mm have centres 25 mm apart. What is their relationship?

  1. They are externally tangent
  2. They are concentric
  3. They intersect at two points
  4. They are internally tangent Correct answer.

Explanation

The difference of the radii is 25 mm, which equals the centre distance, so the smaller circle touches the larger internally. Internal tangency occurs exactly when the centre distance equals the difference of the radii.

Question 41Geometrical construction and plane geometry

Which method constructs a regular polygon by first dividing a diameter into equal parts and then using arcs from the ends of the diameter?

  1. The concentric-circle method for ellipses
  2. The involute construction for gear teeth
  3. The trammel method for ellipses
  4. The general method for inscribing any regular polygon in a circle Correct answer.

Explanation

The general polygon construction divides a diameter into the required number of equal parts and strikes arcs from the ends of the diameter to locate the vertices on the circle. It works for any number of sides and is widely used for heptagons and nonagons.

Question 42Geometrical construction and plane geometry

A straight line AB is to be divided into seven equal parts using only a ruler and compasses. Which construction is used to locate the division points on AB?

  1. Draw a ray from A, step off seven equal divisions along it, join the last point to B, then draw parallels to that joining line through the other division points. Correct answer.
  2. Bisect AB repeatedly, then subdivide each half by trial until seven equal lengths are obtained.
  3. Draw a circle centred on A with radius AB and step the chord of one-seventh of the circumference along AB.
  4. Construct the perpendicular bisector of AB and divide each half into 3.5 parts by eye.

Explanation

Equal division of a line uses the intercept theorem: equal steps on an auxiliary ray produce equal intercepts on AB when parallels are drawn to the closing line. The parallels transfer the ratio from the inclined ray onto AB. This works for any number of parts and needs only a set square and straightedge.

Question 43Geometrical construction and plane geometry

An angle of 75 degrees is to be constructed at a point on a straight line using compasses only for the angular work. Which combination of basic constructions gives 75 degrees?

  1. Construct 60 degrees, then bisect the 30-degree remainder twice.
  2. Construct 45 degrees, then add one-third of a 90-degree angle.
  3. Construct 90 degrees, then bisect the 30-degree remainder between 60 and 90 degrees. Correct answer.
  4. Construct 60 degrees, then add one-quarter of a 60-degree angle.

Explanation

A 90-degree angle is built by erecting a perpendicular, and 60 degrees by stepping the radius. The gap between them is 30 degrees; bisecting that gap once gives 15 degrees, so 60 + 15 = 75 degrees. Every step is a standard bisection or perpendicular erection.

Question 44Geometrical construction and plane geometry

A regular hexagon is to be inscribed in a circle of radius 40 mm. What is the length of each side of the hexagon, and why?

  1. About 34.6 mm, because the side equals R times the sine of 60 degrees.
  2. 40 mm, because the side of an inscribed regular hexagon equals the radius of the circumscribing circle. Correct answer.
  3. About 56.6 mm, because the side equals R times the square root of 2.
  4. 80 mm, because the side equals the diameter of the circle.

Explanation

A regular hexagon is made of six equilateral triangles meeting at the centre, so each side equals the radius. Stepping the radius around the circumference therefore divides it into six equal parts. For R = 40 mm the side is 40 mm.

Question 45Geometrical construction and plane geometry

Two circles of radii 35 mm and 20 mm have their centres 55 mm apart. Which statement describes their relationship?

  1. They are internally tangent to each other.
  2. They are externally tangent to each other. Correct answer.
  3. They are separate and do not touch.
  4. They intersect at two points.

Explanation

The sum of the radii is 35 + 20 = 55 mm, which equals the centre distance. When the centre distance equals the sum of the radii, the circles touch externally at a single point on the line of centres.

Question 46Geometrical construction and plane geometry

A cycloid is to be drawn for a generating circle of radius r rolling along a straight line. Which statement correctly describes the curve and its construction?

  1. The curve has a maximum height of 2 pi r and repeats every r along the base.
  2. The curve has a maximum height of r above the base line and repeats every pi r.
  3. The curve is a straight line of length 2 pi r, because the rolling circle traces its diameter.
  4. The curve has a maximum height of 2r above the base line and one complete arch spans 2 pi r along the base. Correct answer.

Explanation

A point on the rim of a circle of radius r rolling on a straight line rises to a height of 2r (the diameter) at the top of the arch. One complete revolution carries the circle forward by the circumference, 2 pi r, so each arch spans that distance along the base line.

Question 47Orthographic projection (first and third angle)

In a third-angle orthographic layout, where is the top view placed relative to the front view?

  1. Above the front view Correct answer.
  2. To the left of the front view
  3. To the right of the front view
  4. Below the front view

Explanation

Third-angle projection places each view on the side of the front view corresponding to the direction from which it is seen, so the top view sits above the front view and the right-side view sits to its right.

Question 48Orthographic projection (first and third angle)

A drawing shows the front view with the top view directly beneath it and the side view on the far side of the top view. Which projection system is being used?

  1. Third-angle projection
  2. First-angle projection Correct answer.
  3. Perspective projection
  4. Isometric projection

Explanation

In first-angle projection the object is placed between the observer and the projection plane, so the top view falls below the front view and the side view is displaced away from the front view. This arrangement is the standard first-angle layout.

Question 49Orthographic projection (first and third angle)

What does the standard projection symbol placed near the title block indicate?

  1. The revision number of the sheet
  2. The material specification of the part
  3. The drawing scale ratio
  4. The projection system used for the drawing Correct answer.

Explanation

The projection symbol is a truncated cone drawn in two views; its arrangement shows whether the drawing uses first-angle or third-angle projection. It is a convention identifier read independently of the title block data.

Question 50Orthographic projection (first and third angle)

In first-angle projection, the view obtained by looking at the object from the left is drawn on which side of the front view?

  1. Directly above
  2. The right side Correct answer.
  3. The left side
  4. Directly below

Explanation

First angle projects the object onto the plane beyond it, so a view seen from the left is projected onto the right-hand plane and appears to the right of the front view. The layout is thus reversed compared with third angle.