WAEC 2020 · Paper 2 · Q10

(a)
The ratio of the radius ( $r$ ) of the base of a cone to the height ( $h$ ) is $2 : 3$ . If the height of the cone is $8.1\text{ cm}$ , calculate, correct to one decimal place, the volume of the cone. $\left[\text{Take }\pi = \frac{22}{7}\right]$
(b)
Mr. Uduh invested an amount of money in two separate finance firms in the ratio $3 : 5$ . His profit was calculated on $8\%$ and $10\%$ rate of simple interest respectively. If after a year, he received a sum of ₦92,000.00 as total interest, calculate, correct to the nearest whole number, the total amount invested.

Worked solution (try it first)

$r : h = 2 : 3$ , so $r = \frac23 \times 8.1 = 5.4$ cm.
Volume $= \frac13 \times \frac{22}{7} \times 5.4^2 \times 8.1$
$\approx 247.4\text{ cm}^3$ .

Let the total be $y$ .
The two parts are $\frac38 y$ at $8\%$ and $\frac58 y$ at $10\%$ , so one year's interest is $\frac38 y \times 0.08 + \frac58 y \times 0.10 = 0.03y + 0.0625y$
$= 0.0925y$ .
$0.0925y = 92\,000$ , so $y \approx ₦994,595$ to the nearest naira.