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WAEC Mathematics 2021 Paper

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Question : 26

Total: 49

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.

r = h
r = √ $\;\frac{3h^2}{\pi}$
r = πh
r = h √ $\;\frac{3}{h}$

Solution:

Volume of cube = H. H. H. = H $^3$

the volume of a cone is, V= $\;\frac{1}{3}$ πr $^2$ h.

Volume of cube = the volume of a cone

H $^3$ = $\;\frac{1}{3}$ πr $^2$ h.

$\;\frac{3H^3}{\pi h}$ = r $^2$

√ $\;\frac{3H^3}{\pi h}$ = r

h √ $\;\frac{3H^2}{\pi}$ = r

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