How many spherical lead shots each of diameter $ 4.2 \mathrm{~cm} $ can be obtained from a solid rectangular lead piece with dimensions $ 66 \mathrm{~cm} \times 42 \mathrm{~cm} \times 21 \mathrm{~cm} $.

Given:

Diameter of each spherical lead shot $=4.2\ cm$

Dimensions of solid rectangular lead piece are \( 66 \mathrm{~cm} \times 42 \mathrm{~cm} \times 21 \mathrm{~cm} \).

To do:

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

Solution:

Radius of each spherical lead $=\frac{4.2}{2}\ cm$

$=2.1\ cm$

This implies,

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

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

$=\frac{4\pi}{3} \times 2.1 \times 2.1 \times 2.1$

Volume of the solid rectangular lead piece $=lbh$

$=66\times42\times21$

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

$=\frac{66\times42\times21}{\frac{4\pi}{3} \times 2.1 \times 2.1 \times 2.1}$

$=3\times2\times250$

$=6\times250$

$=1500$

The number of spherical lead shots that can be obtained is 1500. 

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Updated on: 10-Oct-2022

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