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Maharashtra HSC Workshop Science & Calculation study materials
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Maharashtra HSC Workshop Science & Calculation practice questions

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Question 1Workshop Safety, Tools and Measuring Instruments

In a workshop fitting shop, which personal protective equipment is specifically intended to protect the eyes while using a pedestal grinding machine?

  1. Ear plugs
  2. Cotton apron
  3. Safety goggles or a face shield Correct answer.
  4. Leather hand gloves

Explanation

Grinding throws high-speed abrasive particles and sparks toward the face, so eye protection rated for impact is mandatory. Safety goggles or a full face shield intercept these flying particles before they reach the cornea. Gloves, ear plugs and aprons serve other protective purposes and do not shield the eyes.

Question 2Workshop Safety, Tools and Measuring Instruments

A fitter must remove a tightly rusted nut without damaging its flats. Which tool is the correct choice for this task?

  1. Chisel and hammer
  2. Pipe wrench
  3. Adjustable wrench
  4. Ring spanner Correct answer.

Explanation

A ring spanner grips all six flats of the nut, so the tightening force is distributed and the corners are not rounded off. It also resists slipping better than an open-ended or adjustable tool on a seized fastener. A pipe wrench or chisel would mark and deform the nut.

Question 3Workshop Safety, Tools and Measuring Instruments

On a steel rule graduated in millimetres, the smallest division marked is 0.5 mm. What is the least count of this rule?

  1. 1 mm
  2. 5 mm
  3. 0.5 mm Correct answer.
  4. 0.05 mm

Explanation

The least count of a graduated scale equals the value of its smallest marked division. Since the finest graduation on this rule represents half a millimetre, the least count is 0.5 mm. Values such as 0.05 mm belong to instruments with a vernier or micrometer scale, not to a plain rule.

Question 4Workshop Safety, Tools and Measuring Instruments

Which fire extinguisher is the correct first response for a small fire in a pan of burning lubricating oil on a workshop bench?

  1. Water (stored pressure) type
  2. Dry sand bucket only
  3. Foam type
  4. Carbon dioxide type Correct answer.

Explanation

Burning oil is a class B flammable-liquid fire, and carbon dioxide smothers it without leaving residue or conducting electricity. CO2 also cools locally and does not spread the burning liquid as a water jet would. Water is dangerous here because it flashes to steam and ejects burning oil.

Question 5Workshop Safety, Tools and Measuring Instruments

What is the primary purpose of a centre punch when used before drilling a hole in a mild steel plate?

  1. To measure the depth of the hole
  2. To deburr the drilled edge
  3. To enlarge the hole after drilling
  4. To make an indentation that locates and guides the drill point Correct answer.

Explanation

A centre punch produces a small conical dimple at the marked centre so the drill point does not wander on the flat surface. This indentation acts as a seat that starts the drill accurately. A prick punch is used first for layout, and the centre punch deepens the mark before drilling.

Question 6Workshop Safety, Tools and Measuring Instruments

A vernier calliper reads a main-scale value of 23 mm and the 6th vernier division coincides with a main-scale line. If the least count is 0.02 mm, what is the measured dimension?

  1. 23.60 mm
  2. 23.12 mm Correct answer.
  3. 23.06 mm
  4. 23.02 mm

Explanation

The vernier reading equals the coinciding division number multiplied by the least count, here 6 × 0.02 = 0.12 mm. Adding this to the main-scale value gives 23 + 0.12 = 23.12 mm. This is the standard method for reading any vernier scale.

Question 7Workshop Safety, Tools and Measuring Instruments

Why must the spindle of a micrometer be brought onto the workpiece using the ratchet stop rather than the thimble?

  1. The ratchet gives a constant measuring force and prevents over-tightening Correct answer.
  2. The ratchet compensates for temperature expansion of the frame
  3. The ratchet increases the measuring range of the instrument
  4. The ratchet locks the spindle so the reading cannot change

Explanation

The ratchet stop slips at a preset torque, so every measurement is taken with the same light contact pressure. Using the thimble directly can crush thin work or spring the frame, giving false readings. Consistent force is essential for repeatable micrometer results.

Question 8Workshop Safety, Tools and Measuring Instruments

A surface plate is used in the fitting shop mainly for which purpose?

  1. Measuring the hardness of metals
  2. Bending sheet metal to shape
  3. Grinding the edges of tools
  4. Providing a flat reference surface for marking and inspection Correct answer.

Explanation

A surface plate is machined and lapped to a very flat plane, giving a true datum for scribing lines and checking flatness. Height gauges and V-blocks rest on it so measurements refer to a single flat reference. It is a reference surface, not a forming or hardness-testing device.

Question 9Workshop Safety, Tools and Measuring Instruments

During a hacksawing operation, the blade breaks repeatedly near the pin holes. Which cause best explains this failure?

  1. Too many teeth per inch for the material
  2. Insufficient cutting fluid on the blade
  3. Using a blade of the correct length
  4. Excessive blade tension combined with a twisted frame Correct answer.

Explanation

Over-tensioning a hacksaw blade, especially when the frame is not straight, concentrates stress at the pin holes where the blade is weakest. That stress leads to fatigue cracking at the ends. Correct tension is firm but allows a slight flex, and the frame must be aligned with the cut.

Question 10Workshop Safety, Tools and Measuring Instruments

Which safety precaution is essential before changing a grinding wheel on a bench grinder?

  1. Wear loose clothing to work quickly
  2. Run the machine at full speed to check the old wheel
  3. Isolate the machine from the power supply and allow the wheel to stop Correct answer.
  4. Remove the wheel guard to improve access

Explanation

Locking off the supply prevents accidental starting while hands are inside the machine. Letting the wheel come to a complete stop avoids contact with a coasting abrasive disc. The guard must stay fitted, and loose clothing is never worn near rotating machinery.

Question 11Workshop Safety, Tools and Measuring Instruments

A depth micrometer is used to check the depth of a blind hole. What must be done to obtain a correct reading?

  1. Add the frame size to the thimble reading
  2. Use the ratchet to force the rod against the bottom
  3. Subtract the thimble reading from the barrel range
  4. Read the thimble directly, since the scale starts at zero at the reference face Correct answer.

Explanation

In a depth micrometer the measuring rod protrudes from the reference face when the thimble reads zero, so the thimble scale directly indicates how far the rod extends. The reading is therefore taken as shown, without adding or subtracting a frame size. The ratchet is used to seat the rod with consistent light force.

Question 12Workshop Safety, Tools and Measuring Instruments

What is the function of the try square in a fitting shop?

  1. Measuring the length of a shaft
  2. Measuring the pitch of a screw thread
  3. Checking and marking right angles and straightness Correct answer.
  4. Cutting internal keyways

Explanation

A try square has a stock and blade set at exactly 90 degrees, so it checks whether an edge is square to a face and marks perpendicular lines. Its blade also reveals straightness against a surface. It is an angular checking tool, not a length or thread gauge.

Question 13Workshop Safety, Tools and Measuring Instruments

A vernier height gauge is set on a surface plate to scribe a line at 45 mm. Which setup error would cause the scribed line to be higher than intended?

  1. Tilting the scriber slightly away from the work
  2. Placing the workpiece on a thin packing sheet
  3. Zero error where the vernier reads zero when the scriber is above the plate Correct answer.
  4. Using a worn scriber point

Explanation

The height gauge is read relative to the surface plate, so a positive zero error means every setting is higher than the indicated value. The scriber would then mark above 45 mm. Zero error must be checked and corrected before use.

Question 14Workshop Safety, Tools and Measuring Instruments

Which tool is most suitable for measuring the outside diameter of a thin sheet-metal wire accurately?

  1. Try square
  2. Vernier height gauge
  3. Steel rule
  4. Outside micrometer Correct answer.

Explanation

An outside micrometer measures small diameters between flat anvil and spindle faces with a fine least count, typically 0.01 mm. This resolution is needed for thin wire, where a rule cannot give a reliable reading. The height gauge and try square are not designed for round-section diameter measurement.

Question 15Workshop Safety, Tools and Measuring Instruments

What does a feeler gauge measure in engine and machine assembly work?

  1. The clearance gap between two assembled surfaces Correct answer.
  2. The hardness of a bearing surface
  3. The torque applied to a bolt
  4. The surface roughness of a machined face

Explanation

A feeler gauge is a set of thin blades of known thickness used to check the gap between mating parts, such as valve clearances or bearing clearances. The blade that just slides through indicates the gap size. It measures clearance, not hardness, torque or roughness.

Question 16Workshop Safety, Tools and Measuring Instruments

A worker must lift a heavy machine vice from the floor to a bench. Which practice follows correct manual-handling and workshop safety principles?

  1. Lift with a bent back and straight legs to keep the load close
  2. Lift alone and hurry to reduce exposure time
  3. Use a hoist or ask a second person, keeping the back straight and load close to the body Correct answer.
  4. Twist the trunk while lifting to place the vice quickly

Explanation

Heavy items such as a machine vice should be moved mechanically or with help, because the load exceeds safe manual limits. When manual lifting is unavoidable, the back is kept straight, knees bent and the load close to the body. Twisting under load is a major cause of back injury.

Question 17Workshop Safety, Tools and Measuring Instruments

A 0-25 mm outside micrometer has a barrel with 0.5 mm graduations and a thimble with 50 divisions. What is its least count?

  1. 0.05 mm
  2. 0.5 mm
  3. 0.01 mm Correct answer.
  4. 0.001 mm

Explanation

The thimble makes one full turn per 0.5 mm of spindle travel, so each of its 50 divisions represents 0.5 ÷ 50 = 0.01 mm. This is the standard least count of a metric micrometer. Finer values require a vernier micrometer attachment.

Question 18Workshop Safety, Tools and Measuring Instruments

Which of the following is the correct method for storing a precision vernier calliper after use?

  1. Hang it by the jaws on a hook above the bench
  2. Store it with the jaws fully closed and locked in a toolbox with other tools
  3. Close the jaws tightly on the workpiece and leave it there
  4. Wipe clean, lightly oil the beam and store in its case with jaws slightly open Correct answer.

Explanation

Cleaning removes abrasive grit, light oil prevents corrosion, and storing in the case protects the measuring faces from knocks. Leaving the jaws slightly open avoids trapping moisture and prevents face contact damage. Precision instruments should never be stored loose with general tools.

Question 19Workshop Safety, Tools and Measuring Instruments

In a bench-fitting job, a file is found to skid over the work surface instead of cutting. Which cause is most likely?

  1. The file has a single-cut pattern with fine teeth
  2. The file has a smooth second cut
  3. The file teeth are clogged with soft metal, forming pinning Correct answer.
  4. The file is too long for the stroke

Explanation

Soft metals such as aluminium fill the spaces between the teeth, a condition called pinning, so the file rides on the packed metal instead of cutting. The remedy is to clean the file with a file card and chalk the teeth lightly. A single-cut or smooth file still cuts, just more slowly.

Question 20Workshop Safety, Tools and Measuring Instruments

A drill bit is found to have its lip clearance reduced to nearly zero after repeated sharpening. What effect will this have during drilling?

  1. The hole diameter will become undersize by exactly the clearance value
  2. The drill point will rub instead of cut, causing heat and poor penetration Correct answer.
  3. The flutes will eject chips more efficiently
  4. The drill will cut faster with a smoother finish

Explanation

Lip clearance is the relief angle behind the cutting edge that allows the edge to bite into the metal. Without it, the heel of the point rubs on the bottom of the hole, generating heat and preventing penetration. The drill may also squeal and overheat.

Question 21Workshop Safety, Tools and Measuring Instruments

A surface plate is checked with a dial indicator mounted on a height stand. The indicator needle moves by 0.03 mm across a 200 mm span. What does this indicate about the plate?

  1. The plate is perfectly flat and the movement is due to the indicator spring
  2. The plate has a flatness error of about 0.03 mm over that span Correct answer.
  3. The indicator least count is 0.03 mm
  4. The plate hardness varies across the span

Explanation

A dial indicator on a stand traces the surface relative to a fixed base, so any needle movement records a change in height, that is, a departure from flatness. A 0.03 mm swing means the surface deviates by that amount over the measured span. Flatness is thus assessed as the total indicator movement.

Question 22Workshop Safety, Tools and Measuring Instruments

A vernier calliper is used to measure a cylindrical shaft, and the reading is taken with the jaws tilted relative to the axis. What type of error does this introduce and why?

  1. A zero error, because the jaws do not close fully
  2. A systematic error, because the jaws then span a chord shorter than the true diameter Correct answer.
  3. A random error, because the jaws slip on the curved surface
  4. A parallax error, because the scale is viewed at an angle

Explanation

When the jaws are not diametrically opposite, they measure a chord of the circular section, which is always shorter than the true diameter. Because the tilt is repeated in the same direction, the resulting error is systematic and biases readings low. Correct technique aligns the jaws across the diameter.

Question 23Workshop Safety, Tools and Measuring Instruments

During thread measurement with a screw pitch gauge, a blade marked 1.5 fits the thread perfectly. What does this value represent, and how is the pitch related to it?

  1. It represents the major diameter in millimetres
  2. It represents the pitch in millimetres, the axial distance between corresponding points on adjacent threads Correct answer.
  3. It represents the number of threads per centimetre
  4. It represents the thread angle in degrees

Explanation

Screw pitch gauge blades are marked with the pitch, the axial distance from one thread crest to the next corresponding crest. A 1.5 blade therefore matches a thread of 1.5 mm pitch. Pitch is not the diameter or the flank angle, which are measured by other means.

Question 24Workshop Safety, Tools and Measuring Instruments

A workshop stores oxygen and acetylene cylinders together in a corner near a heater. Which combination of faults makes this storage unsafe?

  1. Cylinders are full and the store is indoors
  2. The store has a concrete floor and good ventilation
  3. Fuel gas and oxidant are stored together and close to a heat source Correct answer.
  4. The cylinders are upright and chained

Explanation

Oxygen and fuel gas must be segregated so a leak from one cannot feed a fire involving the other, and both must be kept away from heat that raises internal pressure. Storing them together beside a heater combines both faults and greatly increases the risk of a violent fire or cylinder rupture. Upright, chained cylinders in a ventilated store are correct practice.

Question 25Engineering Materials and Material Properties

In a tensile test on a mild steel specimen, the stress at which the linear elastic region ends and measurable permanent strain begins is called the:

  1. Fracture stress
  2. Proportional limit stress
  3. Ultimate tensile stress
  4. Yield stress Correct answer.

Explanation

The yield stress marks the onset of appreciable plastic deformation, commonly identified by the upper yield point or the 0.2 percent offset construction. Beyond this value the specimen deforms permanently, so it is the design-relevant strength measure for ductile workshop metals.

Question 26Engineering Materials and Material Properties

A workshop bar of length 500 mm is heated uniformly and its temperature rises by 60 degrees Celsius. Taking the coefficient of linear expansion as 12 x 10^-6 per degree Celsius, the free expansion of the bar is:

  1. 0.72 mm
  2. 0.36 mm
  3. 3.6 mm Correct answer.
  4. 0.036 mm

Explanation

Free thermal expansion is calculated as change in length equals original length times coefficient of expansion times temperature rise. Substituting 500 mm, 12 x 10^-6 and 60 gives 0.36 mm only if the decimal place is misplaced, so the correct value is 3.6 mm.

Question 27Engineering Materials and Material Properties

Which property of a material describes its ability to absorb energy up to the point of fracture under impact loading?

  1. Hardness
  2. Stiffness
  3. Toughness Correct answer.
  4. Malleability

Explanation

Toughness is the total energy absorbed per unit volume before fracture, represented by the area under the stress-strain curve. A tough material combines adequate strength with significant ductility, which is why it resists sudden impact without brittle failure.

Question 28Engineering Materials and Material Properties

A brinell hardness test is performed using a 10 mm diameter hardened steel ball and a test load of 3000 kgf. The resulting hardness number is calculated from the:

  1. Diagonal length of a square pyramid impression
  2. Rebound height of a falling hammer
  3. Depth of the diamond indentation
  4. Diameter of the recovered spherical impression Correct answer.

Explanation

The brinell hardness number is the applied load divided by the curved surface area of the spherical impression, which is derived from the measured impression diameter. Hence the ball diameter and load must both be quoted along with the reading.

Question 29Engineering Materials and Material Properties

In a simple tensile test, engineering strain is calculated as:

  1. Load divided by original cross-sectional area
  2. Change in length divided by original gauge length Correct answer.
  3. Change in length divided by instantaneous length
  4. Extension multiplied by original gauge length

Explanation

Engineering strain uses the original gauge length as the reference, so it equals the extension divided by that original length. True strain, by contrast, uses the instantaneous length and is preferred once deformation becomes large.

Question 30Engineering Materials and Material Properties

Which type of cast iron is produced by adding a small amount of magnesium or cerium to the molten iron before casting, giving graphite in a nodular form?

  1. Malleable cast iron
  2. Spheroidal graphite iron Correct answer.
  3. Grey cast iron
  4. White cast iron

Explanation

Magnesium or cerium acts as a nodularising agent so that the carbon precipitates as spheroids rather than flakes, producing spheroidal graphite iron. The rounded graphite gives markedly higher ductility and tensile strength than grey cast iron.

Question 31Engineering Materials and Material Properties

A steel shaft of original length 200 mm is loaded in tension and extends by 0.20 mm while remaining elastic. Using a Young's modulus of 200 GPa, the tensile stress induced in the shaft is:

  1. 100 MPa
  2. 200 MPa Correct answer.
  3. 400 MPa
  4. 20 MPa

Explanation

Strain equals extension divided by original length, giving 0.20 divided by 200, which is 0.001. Multiplying strain by Young's modulus of 200 GPa gives 200 MPa, and this is well below the yield strength of common steels.

Question 32Engineering Materials and Material Properties

A cylindrical specimen of diameter 10 mm is pulled with a load of 15.7 kN. Taking pi as 3.14, the engineering stress in the specimen is closest to:

  1. 200 MPa Correct answer.
  2. 500 MPa
  3. 100 MPa
  4. 50 MPa

Explanation

The cross-sectional area equals pi times diameter squared divided by four, giving 78.5 square millimetres. Dividing the 15.7 kN load by this area yields 200 newtons per square millimetre, that is 200 MPa.

Question 33Engineering Materials and Material Properties

The main purpose of normalising a plain carbon steel component after hot working is to:

  1. Transform the surface layer into martensite
  2. Produce a uniform fine pearlite structure and relieve internal stresses Correct answer.
  3. Increase surface carbon content for wear resistance
  4. Soften the steel to the lowest possible hardness for machining

Explanation

Normalising involves heating above the upper critical temperature and cooling in still air, which refines the grain and gives a uniform ferrite-pearlite structure with stresses relieved. It is often used to condition steel before machining or before a final hardening operation.

Question 34Engineering Materials and Material Properties

A specimen of gauge length 50 mm is tested and fractures with a final gauge length of 62 mm. The percentage elongation is:

  1. 31 percent
  2. 24 percent Correct answer.
  3. 20 percent
  4. 12 percent

Explanation

Percentage elongation is the increase in gauge length divided by the original gauge length, multiplied by 100. Here the increase is 12 mm on 50 mm, giving 24 percent, which is a standard measure of ductility.

Question 35Engineering Materials and Material Properties

In a tensile test, a material shows a high proportional limit, a small percentage elongation and a fracture surface without visible necking. The material is best described as:

  1. Perfectly plastic
  2. Brittle and relatively strong Correct answer.
  3. Highly malleable
  4. Ductile and tough

Explanation

Little elongation, no necking and a flat fracture surface indicate brittle behaviour, while the high proportional limit shows useful strength before failure. Such materials absorb little energy in impact and give no visible warning before fracture.

Question 36Engineering Materials and Material Properties

The critical cooling rate during quenching of a steel is the minimum rate that:

  1. Prevents any hardening from taking place
  2. Causes the steel to remain austenitic at room temperature
  3. Allows complete transformation to coarse pearlite
  4. Produces a fully martensitic structure by avoiding the pearlite and bainite noses of the TTT curve Correct answer.

Explanation

If the steel is cooled faster than the critical rate, the cooling curve misses the nose of the time-temperature-transformation diagram and austenite transforms to martensite. Alloying elements that shift the curve to the right lower the critical rate and make thick sections easier to harden.

Question 37Engineering Materials and Material Properties

Which non-ferrous metal is chosen for workshop components requiring high electrical conductivity combined with good cold-working ductility, and is commonly used for busbars and wiring?

  1. Aluminium
  2. Lead
  3. Zinc
  4. Copper Correct answer.

Explanation

Copper offers the highest practical electrical conductivity among common structural metals after silver, and it cold-works readily into wire and busbar. Aluminium is lighter and cheaper per unit mass but has lower conductivity for the same cross-section.

Question 38Engineering Materials and Material Properties

A machine component must resist wear on its surface while remaining tough in its core. The most suitable treatment for a low carbon steel part is:

  1. Normalising only
  2. Full annealing
  3. Carburising followed by quenching and tempering Correct answer.
  4. Stress relieving after welding

Explanation

Carburising diffuses carbon into the surface so that quenching hardens the case while the low carbon core stays tough. This combination of a hard wear-resistant skin and a ductile core suits gears, shafts and similar components.

Question 39Engineering Materials and Material Properties

A steel component has a yield strength of 400 MPa and is designed with a factor of safety of 2.5 on yield. The maximum permissible working stress is:

  1. 1000 MPa
  2. 160 MPa Correct answer.
  3. 250 MPa
  4. 400 MPa

Explanation

The working stress is the yield strength divided by the factor of safety, so 400 divided by 2.5 gives 160 MPa. This margin keeps the component elastic under service loads and covers uncertainties in loading and material properties.

Question 40Engineering Materials and Material Properties

Which statement correctly distinguishes hardness from tensile strength for a plain carbon steel?

  1. Hardness depends only on the surface finish, while tensile strength depends only on the specimen length
  2. Hardness is measured by resistance to indentation, while tensile strength is measured by resistance to axial pulling to fracture Correct answer.
  3. Hardness and tensile strength are the same physical quantity measured in the same units
  4. Tensile strength is measured by indentation, while hardness is measured by pulling a specimen to fracture

Explanation

Hardness is a localised surface property assessed by indentation or scratching, whereas tensile strength is a bulk property obtained from a tensile test to fracture. For many steels the two correlate empirically, which is why hardness tests are used as quick shop-floor checks.

Question 41Engineering Materials and Material Properties

A steel wire of original length 2 m and cross-sectional area 2 square millimetres carries a tensile load of 800 N. Taking Young's modulus as 200 GPa, the elastic extension is:

  1. 4 mm Correct answer.
  2. 0.4 mm
  3. 40 mm
  4. 0.04 mm

Explanation

Stress equals 800 N divided by 2 square millimetres, giving 400 MPa, and strain equals 400 MPa divided by 200 GPa, giving 0.002. Multiplying strain by the 2000 mm length gives 4 mm of elastic extension.

Question 42Engineering Materials and Material Properties

Two steel specimens of the same composition are quenched, one in water and one in oil. Compared with the oil-quenched specimen, the water-quenched specimen will generally show:

  1. A fully annealed structure with coarse pearlite
  2. Higher hardness with a greater risk of distortion and cracking Correct answer.
  3. Lower hardness with improved toughness throughout
  4. Identical hardness because the cooling medium does not affect hardening

Explanation

Water gives a much higher heat extraction rate than oil, so the cooling curve more easily misses the transformation nose and produces more martensite. The resulting higher hardness is accompanied by larger thermal and transformation stresses, raising the risk of quench cracks and distortion.

Question 43Engineering Materials and Material Properties

A component is required to operate at elevated temperature under steady load without progressive deformation over long periods. The material property that most directly governs this requirement is:

  1. Magnetic permeability
  2. Creep resistance Correct answer.
  3. Electrical resistivity
  4. Impact toughness

Explanation

Creep is time-dependent plastic deformation under sustained stress at elevated temperature, so creep resistance governs long-term dimensional stability. Creep-resistant alloys use high melting point elements and stable precipitates to slow dislocation motion at temperature.

Question 44Engineering Materials and Material Properties

A cylindrical aluminium bar of diameter 20 mm and length 100 mm is compressed axially by a load of 31.4 kN. Taking pi as 3.14 and Young's modulus as 70 GPa, the magnitude of the elastic shortening is closest to:

  1. 0.28 mm
  2. 0.14 mm Correct answer.
  3. 0.014 mm
  4. 1.4 mm

Explanation

The area is pi times 20 squared divided by four, giving 314 square millimetres, so the compressive stress is 31400 N divided by 314 square millimetres, about 100 MPa. Strain is 100 MPa divided by 70 GPa, about 0.00143, and multiplying by the 100 mm length gives roughly 0.14 mm.

Question 45Applied Workshop Calculations (length, area, volume, mass, density)

A workshop bench top measures 1.8 m by 75 cm. What is its area in square metres?

  1. 0.135 m²
  2. 1.35 m² Correct answer.
  3. 13.5 m²
  4. 135 m²

Explanation

Convert 75 cm to 0.75 m first, because area needs both dimensions in the same unit. Multiplying 1.8 m by 0.75 m gives 1.35 m². Forgetting the conversion is the usual source of a tenfold error here.

Question 46Applied Workshop Calculations (length, area, volume, mass, density)

A steel bar has a mass of 4.68 kg and a volume of 600 cm³. What is its density in g/cm³?

  1. 0.78
  2. 78
  3. 0.078
  4. 7.8 Correct answer.

Explanation

Density equals mass divided by volume, so first convert 4.68 kg to 4680 g. Dividing 4680 g by 600 cm³ gives 7.8 g/cm³, which is the familiar figure for steel. Mixing kilograms with cubic centimetres without converting is the common mistake.

Question 47Applied Workshop Calculations (length, area, volume, mass, density)

How many millimetres are there in 2.35 m?

  1. 23500 mm
  2. 235 mm
  3. 23.5 mm
  4. 2350 mm Correct answer.

Explanation

One metre contains 1000 millimetres, so multiply by 1000. Shifting the decimal point three places to the right on 2.35 gives 2350 mm. Moving only two places would give centimetres rather than millimetres.

Question 48Applied Workshop Calculations (length, area, volume, mass, density)

A cylindrical pin has a diameter of 12 mm and a length of 50 mm. Using π = 3.14, what is its volume in mm³?

  1. 1884 mm³
  2. 22608 mm³
  3. 5652 mm³ Correct answer.
  4. 11304 mm³

Explanation

The radius is half the diameter, so r = 6 mm. Volume equals πr²h, that is 3.14 × 36 × 50 = 5652 mm³. Using the diameter in place of the radius is the standard trap in this calculation.

Question 49Applied Workshop Calculations (length, area, volume, mass, density)

A rectangular plate of mild steel measures 250 mm × 120 mm × 8 mm. Taking the density of mild steel as 7.85 g/cm³, what is the mass of the plate?

  1. 1.884 kg Correct answer.
  2. 188.4 kg
  3. 18.84 kg
  4. 0.1884 kg

Explanation

The volume is 250 × 120 × 8 = 240 000 mm³, which equals 240 cm³. Multiplying 240 cm³ by 7.85 g/cm³ gives 1884 g, or 1.884 kg. Converting cubic millimetres to cubic centimetres before applying density keeps the units consistent.

Question 50Applied Workshop Calculations (length, area, volume, mass, density)

A workshop floor is 6.4 m long and 4.25 m wide. A rectangular machine base occupies 2.5 m² of this floor. What area of floor remains free?

  1. 24.7 m² Correct answer.
  2. 29.7 m²
  3. 21.9 m²
  4. 27.2 m²

Explanation

The floor area is 6.4 × 4.25 = 27.2 m². Subtracting the occupied 2.5 m² leaves 24.7 m² free. Multiplying the dimensions before subtracting is essential, since the machine area is already in square metres.