WAEC 2021 · Paper 1 · Q26

Solid mensuration

A solid brass cube is melted and recast as a solid cone of height $h$ and base radius $r$ . If the height of the cube is $h$ , find $r$ in terms of $h$ .

Worked solution (try it first)

Melting keeps the volume the same: cube $h^3$ = cone $\frac13\pi r^2h$ .
Divide both sides by $h$ and multiply by 3: $3h^2 = \pi r^2$ , so $r^2 = \dfrac{3h^2}{\pi}$ .
Take the square root: $r = \sqrt{\dfrac{3h^2}{\pi}}$ , option B.

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