chapter  13
13 Pages

Volumes of common solids

Problem 1. A cuboid has dimensions of 12 cm by 4 cm by 3 cm. Determine: (a) its volume and (b) its total surface area

The cuboid is similar to Figure 13.1, with l = 12 cm, b = 4 cm and h = 3 cm. (a) Volume of cuboid = l × b × h = 12 × 4 × 3

= 144 cm3 (b) Surface area = 2(bh + hl + lb)

= 2(4 × 3 + 3 × 12 + 12 × 4) = 2(12 + 36 + 48) = 2 × 96 = 192 cm2

Problem 2. An oil tank is the shape of a cube, each edge being of length 1.5 m. Determine: (a) the maximum capacity of the tank in m3 and litres, and (b) its total surface area ignoring input and output

= 1.5 m × 1.5 m × 1.5 m = 1.53 m3 = 3.375 m3

1 m3 = 100 cm × 100 cm × 100 cm = 106 cm3 Hence,

volume of tank = 3.375 × 106 cm3 1 litre = 1000 cm3 hence, oil tank capacity

= 3.375 × 10 6

1000 litres = 3375 litres.