WAEC 2023 · Paper 2 · Q9

(a)
A cylindrical tank of diameter $3.5\text{ m}$ is full of water. Three tankers, each of capacity $6{,}500$ litres, draw water from the tank. Calculate, in metres, correct to two decimal places, the reduction in height of water in the tank. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
The coordinates of two points $P$ and $Q$ in a plane are $(2, -5)$ and $(-4, -6)$ respectively. Find the equation of the straight line joining the points.

Worked solution (try it first)

The tankers take $3 \times 6500 = 19\,500$ litres.
$1\text{ m}^3 = 1000$ litres, so that is $19.5\text{ m}^3$ .
The tank's radius is 1.75 m, so its base is $\frac{22}{7} \times 1.75^2 = 9.625\text{ m}^2$ .
The water removed is a cylinder of that base: $9.625 \times h = 19.5$ , so $h \approx 2.03$ m.