WAEC 2022 · Paper 2 · Q10

(a)
A cylindrical fuel storage tank of diameter $7\text{ m}$ is full of gasoline. If four tankers, each of capacity $13\,500$ litres, draw gasoline from the storage tank, calculate, correct to two decimal places, the height reduction, in metres, of gasoline in the tank. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
Given that $\frac53\sin(x - 29^\circ) = \frac12$ , $0^\circ \le x \le 90^\circ$ , find, correct to the nearest degree, the value of $x$ .

Worked solution (try it first)

The four tankers take $4 \times 13\,500 = 54\,000$ litres.
Since $1000$ litres $= 1\text{ m}^3$ , that is $54\text{ m}^3$ .
The tank's radius is 3.5 m, so a drop of $h$ m removes $\pi r^2h = \frac{22}{7} \times 3.5^2 \times h$
$= 38.5h\text{ m}^3$ .
So $38.5h = 54$ and $h \approx 1.40$ m.

Multiply both sides by $\frac35$ : $\sin(x - 29^\circ) = \frac12 \times \frac35$
$= \frac{3}{10}$ .
So $x - 29^\circ = \sin^{-1} 0.3$
$\approx 17.46^\circ$ , and $x \approx 46.46^\circ \approx 46^\circ$ .