How many spherical bullets each of $5\ cm$ in diameter can be cast from a rectangular block of metal $11\ dm \times 1\ m \times 5\ dm$?

Given:

Dimensions of the rectangular block are $11\ dm \times 1\ m \times 5\ dm$.
Diameter of spherical bullet $=5\ cm$.

To do:

We have to find the number of spherical bullets that can be cast from the rectangular block.

Solution:

Volume of the rectangular block of metal $V_1 = 11 dm \times 10 dm \times 5 dm$    [$1\ m=10\ dm$]

$= 550\ dm^3$

Radius of the spherical bullet $r=\frac{5}{2} \mathrm{~cm}$

Volume of each bullet $V_{2}=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \pi(5)^{3}$

$=\frac{4}{3} \pi \times 125$

$=\frac{500}{3} \times \frac{22}{7}$

$=\frac{11000}{21} \mathrm{~cm}^{3}$
Number of bullets that can be cast $=$ Volume of the rectangular block $\div$ Volume of each bullet

$=\frac{\mathrm{V}_{1}}{\mathrm{~V}_{2}}$

$=\frac{550 \mathrm{dm}^{3}}{\frac{11000}{21} \mathrm{~cm}^{3}}$

$=\frac{550 \times 10 \times 10 \times 10 \times 21}{11000}$          [$1\ dm=10\ cm$]

$=1050$

Therefore, 1050 spherical bullets can be cast from the rectangular block of metal.

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Updated on: 10-Oct-2022

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