WAEC 2017 · Paper 2 · Q11

(a)
It takes 8 students two-thirds of an hour to fill 12 tanks with water. How many tanks of water will 4 students fill in one-third of an hour at the same rate?
(b)
A chord, $20\text{ cm}$ long, is $12\text{ cm}$ from the centre of the circle. Calculate, correct to one decimal place, the: (i) angle subtended by the chord at the centre of the circle; (ii) perimeter of the minor segment cut off by the chord. $\left[\text{Take }\pi = \frac{22}{7}\right]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

The number of tanks is proportional to the number of students and to the time.
Half the students ( $\frac48$ ) for half the time ( $\frac{1/3}{2/3}$ ) fill $12 \times \frac12 \times \frac12 = 3$ tanks.

The perpendicular from the centre to the chord bisects it, making a right-angled triangle with sides 12 cm (the distance) and 10 cm (half the chord).
Half the angle: $\tan\alpha = \frac{10}{12}$ , so $\alpha \approx 39.8^\circ$ and the angle at the centre is $79.6^\circ$ .

The radius is the hypotenuse: $r = \sqrt{12^2 + 10^2}$
$= \sqrt{244}$
$\approx 15.62$ cm.
Arc $= \frac{79.6}{360} \times 2 \times \frac{22}{7} \times 15.62$
$\approx 21.7$ cm.
Perimeter of the segment $=$ arc $+$ chord $= 21.7 + 20 = 41.7$ cm.