# How many spherical bullets each of 5 cm in diameter

Question:

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

Solution:

We are given a metallic block of dimension $=11 \mathrm{dm} \times 1 \mathrm{~m} \times 5 \mathrm{dm}$

We know that, $1 \mathrm{dm}=10^{-1} \mathrm{~m}$

So, the volume of the given metallic block is

$=11 \times 10^{-1} \times 1 \times 5 \times 10^{-1}$

$=55 \times 10^{-2} \mathrm{~m}^{3}$

We want to know how many spherical bullets can be formed from this volume of the metallic block. It is given that the diameter of each bullet should be 5 cm.

We know,

Volume of a sphere $=\frac{4}{3} \pi(r)^{3}$

Here, $r=25 \times 10^{-3} \mathrm{~m}$

Let the no. of bullets formed be n.

We know that the sum of the volumes of the bullets formed should be equal to the volume of the metallic block.

$\Rightarrow 55 \times 10^{-2}=n \times \frac{4}{3} \times \frac{22}{7} \times\left(25 \times 10^{-3}\right)^{3}$

$n=\frac{55 \times 3 \times 7 \times 10^{-2}}{4 \times 22 \times 25 \times 25 \times 25 \times 10^{-9}}$

$=\frac{21 \times 10^{7}}{(2 \times 5)^{3} \times 25}$

$=\frac{21 \times 10^{7}}{10^{3} \times 25}$

$=8400$

Hence the no. of bullets that can be formed is 8400.