How many balls, each of radius $1\ cm$, can be made from a solid sphere of lead of radius $8\ cm$?

Given:

Radius of solid sphere of lead $=8\ cm$.
Radius of each ball $=1\ cm$

To do:

We have to find the number of balls that can be made from the solid sphere.

Solution:

Radius of the solid sphere $R=8 \mathrm{~cm}$

This implies,

Volume of the solid sphere ${V}_{1}=\frac{.4}{3} \pi \mathrm{R}^{3}$

$=\frac{4}{3} \pi(8)^{3}$

$=\frac{4}{3} \pi \times 512$

$=\frac{2048 \pi}{3} \mathrm{~cm}^{3}$
Radius of each small ball $r=1 \mathrm{~cm}$

This implies,

Volume of each small ball ${V}_{2}=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi(1)^{3}$

$=\frac{4}{3} \pi \mathrm{cm}^{3}$

Therefore,

Number of balls that can be made $=$ Volume of the solid sphere $\div$ Volume of each small ball

$=\frac{V_{1}}{V_{2}}$

$=\frac{\frac{2048 \pi}{3}}{\frac{4}{3} \pi r^{3}}$

$=\frac{2048 \pi}{3} \times \frac{3}{4 \pi}$

$=512$

Therefore, 512 balls can be made from the solid sphere.

Tutorialspoint

Updated on: 10-Oct-2022

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