ABSTRACT
A summary of volumes and surface areas of regular solids is shown in Table 19.1.
Problem 1. A water tank is the shape of a rectangular prism having length 2 m, breadth 75 cm and height 50 cm. Determine the capacity of the tank in (a) m3 (b) cm3 (c) litres
Volume of rectangular prism D l ð b ð h (see Table 19.1) (a) Volume of tank D 2 ð 0.75 ð 0.5 D 0.75 m3 (b) 1 m3 D 106 cm3, hence
0.75 m3 D 0.75 ð 106 cm3 D 750 000 cm3 (c) 1 litre D 1000 cm3, hence
750 000 cm3 D 750 000 1000
litres D 750 litres
Problem 2. Find the volume and total surface area of a cylinder of length 15 cm and diameter 8 cm
Volume of cylinder D r2h (see Table 19.1) Since diameter D 8 cm, then radius r D 4 cm Hence volume D ð 42 ð 15 D 754 cm3 Total surface area (i.e. including the two ends)
D 2rh C 2r2 D 2 ð ð 4 ð 15 C2 ð ð 42 D 477.5 cm2
Problem 3. Determine the volume (in cm3) of the shape shown in Fig. 19.1.
