WAEC 2022 · Paper 2 · Q5

(a)
The total surface area of a closed cone of radius $3.8\text{ cm}$ is $374\text{ cm}^2$ . Calculate, correct to two decimal places, the volume of the cone. $\left[\text{Take }\pi = \frac{22}{7}\right]$

Worked solution (try it first)

Total surface area of a closed cone $= \pi r^2 + \pi r l$ .
With $r = 3.8$ : $\frac{22}{7} \times 3.8^2 \approx 45.383$ and $\frac{22}{7} \times 3.8 \approx 11.943$ , so $45.383 + 11.943l = 374$ .
Then $11.943l \approx 328.617$ and $l \approx 27.516$ cm.
Height: $h = \sqrt{27.516^2 - 3.8^2}$
$= \sqrt{757.13 - 14.44}$
$\approx 27.252$ cm.
Volume $= \frac13 \times \frac{22}{7} \times 3.8^2 \times 27.252$
$\approx 412.26\text{ cm}^3$ .