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WAEC Mathematics 2011 Paper

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Question : 18

Total: 47

The height of a cylinder is equal to its radius. If the volume is 0.216

\pi \mathrm{m}^3

Calculate the radius.

0.46m
0.60m
0.87m
1.80m

Solution:

Concept:

For a cylinder, volume equals base area times height:

V = \pi r^2 h

. Since height equals radius, the volume becomes

\pi r^3

.

Explanation:

Let the radius be

r

and the height be

h

.

Given that

h = r

.

Volume of cylinder:

V = \pi r^2 h

.

Substitute

h = r

:

V = \pi r^2 \times r = \pi r^3

.

Given

V = 0.216\pi\ \mathrm{m}^3

.

So,

\pi r^3 = 0.216\pi

.

Divide both sides by

\pi

:

r^3 = 0.216

.

Take the cube root:

r = \sqrt[3]{0.216} = 0.60\ \mathrm{m}

.

Hence, the required radius is

0.60\ \mathrm{m}

.

Answer:

B.

0.60\ \mathrm{m}

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