WAEC 2022 · Paper 2 · Q8

(a)
In a class of 60 students, 30 read Literature and 35 read Government. All the students read at least one of the subjects. If a student is selected at random from the class, find the probability that the student reads only one subject.
(b)
A sector of angle $220^\circ$ is removed from a thin circular metal sheet of radius $63\text{ cm}$ . It is then folded with the straight edges meeting to form a right circular cone. Calculate, correct to one decimal place, the: (i) base radius; (ii) volume, of the cone. $\left[\text{Take }\pi = \frac{22}{7}\right]$
Separate values with commas, e.g. 3, −2

Worked solution (try it first)

Every student reads at least one subject, so $30 + 35$ counts the students who read both twice: $30 + 35 - x = 60$ , and $x = 5$ read both.
Literature only $= 30 - 5 = 25$ .
Government only $= 35 - 5 = 30$ .
Only one subject: $25 + 30 = 55$ students, so $P = \frac{55}{60} = \frac{11}{12}$ .

When the sector is folded into a cone, its arc becomes the circumference of the base.
Arc length $= \frac{220}{360} \times 2\pi \times 63$ and base circumference $= 2\pi r$ , so $r = \frac{220}{360} \times 63 = 38.5$ cm.

The radius of the sheet, 63 cm, becomes the slant height of the cone.
Height: $h = \sqrt{63^2 - 38.5^2}$
$= \sqrt{3969 - 1482.25}$
$= \sqrt{2486.75}$
$\approx 49.867$ cm.
Volume $= \frac13\pi r^2 h$
$= \frac13 \times \frac{22}{7} \times 38.5^2 \times 49.867$
$\approx 77\,435.6\text{ cm}^3$ .