How many spherical lead shots of diameter $ 4 \mathrm{~cm} $ can be made out of a solid cube of lead whose edge measures $ 44 \mathrm{~cm} $.

Given:

Diameter of each spherical lead shot $=4\ cm$

Length of the edge of the solid cube of lead $=44\ cm$

To do:

We have to find the number of spherical lead shots that can be obtained.

Solution:

Radius of each spherical lead shot $=\frac{4}{2}\ cm$

$=2\ cm$

This implies,

Volume of each spherical lead shot $= \frac{4}{3} \pi r^3$

$=\frac{4}{3} \pi \times (2)^{3}$

$=\frac{4\pi}{3} \times 8$

$=\frac{32\pi}{3}$

Volume of the solid cube of lead $=s^3$

$=(44)^3$

Number of spherical lead shots that can be obtained $=\frac{\text { Volume of the solid cube of lead }}{\text { Volume of each spherical lead shot }}$

$=\frac{44\times44\times44}{\frac{32\pi}{3}}$

$=11\times21\times11$

$=121\times21$

$=2541$

The number of spherical lead shots that can be obtained is 2541.  

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Updated on: 10-Oct-2022

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