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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:

Concept:

When a solid is melted and recast, its volume remains unchanged.

Explanation:

Volume of the cube with side

h

is:

V_{\text{cube}} = h^3

Volume of the cone with height

h

and base radius

r

is:

V_{\text{cone}} = \frac{1}{3}\pi r^2 h

Equate the two volumes:

h^3 = \frac{1}{3}\pi r^2 h

Multiply both sides by

3

:

3h^3 = \pi r^2 h

Divide both sides by

\pi h

:

r^2 = \frac{3h^2}{\pi}

Take the positive square root:

r = h\sqrt{\frac{3}{\pi}}

Answer:

Option B:

r = h\sqrt{\frac{3}{\pi}}

or

r = \sqrt{\frac{3h^2}{\pi}}

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