Measurement, Area, Surface Area and Volume
Measurement, Area, Surface Area and Volume
This domain tests perimeter and area of plane figures and surface area and volume of solids, including unit conversion.
Core rules
- Rectangle: area = l × b, perimeter = 2(l + b). Square: area = s², perimeter = 4s.
- Triangle: area = ½ × base × height. Circle: area = πr², circumference = 2πr.
- Cuboid: volume = lbh; total surface area = 2(lb + bh + hl). Cube: volume = s³; total surface area = 6s².
- Cylinder: volume = πr²h; curved surface area = 2πrh; total surface area = 2πr(r + h).
- Convert units: 1 m = 100 cm, so 1 m² = 10,000 cm² and 1 m³ = 1,000,000 cm³. Also 1 litre = 1,000 cm³.
Worked example
A cuboid is 10 cm long, 8 cm wide and 5 cm high. Find its volume and total surface area. Volume = l × b × h = 10 × 8 × 5 = 400 cm³. Total surface area = 2(lb + bh + hl) = 2(10×8 + 8×5 + 5×10) = 2(80 + 40 + 50) = 2 × 170 = 340 cm².
Traps
- Diameter is not radius: if d = 14 cm, use r = 7 cm.
- Curved surface area leaves out the two circular ends; total surface area includes them.
- Perimeter is a length (cm), area is in cm², volume in cm³.
- For unit conversion, square and cube the linear factor, not just multiply by 100.