WAEC 2020 · Paper 2 · Q7

(a)
The diagram shows a wooden structure in the form of a cone, mounted on a hemispherical base. The vertical height of the cone is $48\text{ m}$ and the base radius is $14\text{ m}$ . Calculate, correct to three significant figures, the surface area of the structure. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
Five years ago, Musah was twice as old as Sesay. If the sum of their ages is 100, find Sesay's present age.

Worked solution (try it first)

The surface of the structure is the curved surface of the cone plus the curved surface of the hemisphere (the flat circle where they join is hidden).
Slant height of the cone: $l = \sqrt{48^2 + 14^2}$
$= \sqrt{2304 + 196}$
$= \sqrt{2500}$
$= 50\text{ m}$ .
Curved surface of the cone $= \pi r l$
$= \frac{22}{7} \times 14 \times 50$
$= 2200\text{ m}^2$ .
Curved surface of the hemisphere $= 2\pi r^2$
$= 2 \times \frac{22}{7} \times 196$
$= 1232\text{ m}^2$ .
Total $= 2200 + 1232 = 3432\text{ m}^2$ .
Correct to three significant figures: $3430\text{ m}^2$ .

Let Sesay's age now be $x$ years.
Since the ages add up to 100, Musah is $100 - x$ .
Five years ago they were $x - 5$ and $95 - x$ , and Musah was twice as old: $95 - x = 2(x - 5)$ .
Expand: $95 - x = 2x - 10$ .
So $3x = 105$ and $x = 35$ .
Sesay is 35 years old.