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WAEC Mathematics 2016 Paper

Question : 33

Total: 49

Solution:

Concept:

Equate the volume of the sphere to the volume of the cylinder and solve for

r

Explanation:

Volume of a sphere is

\frac{4}{3}\pi r^3

Volume of a cylinder is

\pi R^2 h

, where

R = 3

cm and

h = 4

cm.

So, cylinder volume

= \pi \times 3^2 \times 4 = 36\pi

^3

Given that volumes are equal:

\frac{4}{3}\pi r^3 = 36\pi

Cancel

\pi

from both sides:

\frac{4}{3}r^3 = 36

Multiply both sides by

\frac{3}{4}

r^3 = 27

Taking the cube root:

r = \sqrt[3]{27} = 3

Answer:

r = 3

cm, so the correct option is C.

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