WAEC 2024 · Paper 1 · Q32

Solid mensuration

A cone and a cylinder are of equal volume. The base radius of the cone is twice the radius of the cylinder. What is the ratio of the height of the cylinder to that of the cone?

Worked solution (try it first)

Let the cylinder have radius $r$ and height $h_2$ , and the cone radius $2r$ and height $h_1$ .
Equal volumes: $\frac13\pi(2r)^2h_1 = \pi r^2h_2$ .
Divide both sides by $\pi r^2$ : $\frac43h_1 = h_2$ .
So $h_2 : h_1 = 4 : 3$ , option B.

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