NECO 2022 · Paper 2 · Q10

Solid mensuration
Approximation & error

A composite solid consists of a cone on top of a cylinder. The cone is 8 cm high and its slant height is 10 cm. If the solid is 18 cm high, calculate the volume of the solid correct to 2 significant figures.

(a)
Volume of the solid, to 2 significant figures ( $\text{cm}^3$ ). $\left(\text{Take } \pi = \frac{22}{7}\right)$

Worked solution (try it first)

The cone sits on the cylinder, so they share the same radius $r$ .
Find $r$ from the cone by Pythagoras: $r^2 = 10^2 - 8^2 = 36$ , so $r = 6$ cm.
The height of the cylinder is $18 - 8 = 10$ cm.
Volume of the cylinder: $\pi r^2 h = \frac{22}{7} \times 36 \times 10$
$\approx 1131.4\text{ cm}^3$ .
Volume of the cone: $\frac13 \pi r^2 h = \frac13 \times \frac{22}{7} \times 36 \times 8$
$\approx 301.7\text{ cm}^3$ .
Add them: $1131.4 + 301.7 = 1433.1\text{ cm}^3$ .
To 2 significant figures, the volume of the solid is $1400\text{ cm}^3$ .

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