The diameter of a metallic ball is $ 4.2 \mathrm{~cm} $. What is the mass of the ball, if the density of the metal is $ 8.9 \mathrm{~g} $ per $ \mathrm{cm}^{3} $ ?

Given:

The diameter of a metallic ball is \( 4.2 \mathrm{~cm} \).

The density of the metal is \( 8.9 \mathrm{~g} \) per \( \mathrm{cm}^{3} \).

To do:

We have to find the mass of the ball.

Solution:

Diameter of the metallic ball $= 4.2\ cm$

This implies,

Radius of the metallic ball $r = \frac{4.2}{2}\ cm$

$= 2.1\ cm$

Volume of the metallic ball $=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times(2.1)^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times 2.1 \times 2.1 \times 2.1$

$=38.808 \mathrm{~cm}^{3}$

We know that,

$\text { Density } = \frac{\text { Mass }}{\text { Volume }}$

Mass $=$ Density $\times$ Volume

$=8.9\times38.808\ g$

$=345.3912\ g$

Therefore, the ,mass of the ball is $345.3912\ g$.

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Updated on: 10-Oct-2022

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