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WAEC Physics 2011 Paper

Question : 2

Total: 49

The density P of a spherical ball of diameter d and mass m is given by

Solution:

Concept:

Density is mass divided by volume for the spherical ball.

Explanation:

The volume of a sphere is

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

Since the diameter is

d

, the radius is

r = \frac{d}{2}

Substitute

r = \frac{d}{2}

into the volume formula:

V = \frac{4}{3}\pi \left(\frac{d}{2}\right)^3 = \frac{4}{3}\pi \cdot \frac{d^3}{8} = \frac{\pi d^3}{6}

Density

P

equals mass divided by volume, so

P = \frac{m}{V}

Therefore,

P = \frac{m}{\pi d^3 / 6} = \frac{6m}{\pi d^3}

Answer:

The correct option is C:

P = \frac{6m}{\pi d^3}

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