WAEC 2014 · Paper 2 · Q7

(a)
A spherical tank of diameter $3\text{ m}$ is filled with water from a pipe of radius $30\text{ cm}$ at $0.2\text{ m}$ per second. Calculate, correct to 3 significant figures, the time, in minutes, it takes to fill the tank. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
When $k$ is added to the expression $y^2 - 12y$ , the expression becomes $(y + p)^2$ . Find the values of $p$ and $k$ .
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Work in metres.
The tank has radius 1.5 m: volume $= \frac43 \times \frac{22}{7} \times 1.5^3$
$= \frac{99}{7}$
$\approx 14.14\text{ m}^3$ .
Each second the water in the pipe moves 0.2 m, so it delivers a cylinder of radius 0.3 m and length 0.2 m: $\frac{22}{7} \times 0.3^2 \times 0.2 = \frac{0.396}{7}$
$\approx 0.0566\text{ m}^3$ per second.
Time $= \frac{99/7}{0.396/7}$
$= \frac{99}{0.396}$
$= 250$ seconds $= \frac{250}{60} \approx 4.17$ minutes.