WAEC 2018 · Paper 2 · Q8

(a)
A container in the form of a cone resting on its vertex is full when 4.158 litres of water is poured into it. If the radius of its base is $21\text{ cm}$ , (i) represent the information in a diagram; (ii) calculate the height of the container. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
A certain amount of water is drawn out of the container such that the surface diameter of the water drops to $28\text{ cm}$ . Calculate the volume of the water drawn out.

Worked solution (try it first)

Draw the cone upside down (vertex at the bottom), with base radius 21 cm at the top and height $h$ from the vertex up to the centre of the base.

$4.158$ litres $= 4158\text{ cm}^3$ .
Volume $= \frac13 \times \frac{22}{7} \times 21^2 \times h$
$= 462h$
$= 4158$ , so $h = 9$ cm.

The water left is a smaller cone with the same shape.
Its surface radius is 14 cm, so by similar triangles its depth is $9 \times \frac{14}{21} = 6$ cm.
Its volume is $\frac13 \times \frac{22}{7} \times 14^2 \times 6 = 1232\text{ cm}^3$ .
Water drawn out $= 4158 - 1232 = 2926\text{ cm}^3$ .