Question

How many spherical bullets can be made out of a solid cube of lead whose edge measures 44cm, each bullet being 4cm in diameter.

Answer 1

Hint:
Here we need to find the number of spherical bullets that can be made out of a cube of lead. For that, we will first assume the number of spherical bullets to be any variable $n$ and then we will find the volume of spherical bullet having diameter 4cm and then we will multiply the value of one spherical bullet by $n$ to calculate the volume of total number of spherical bullets. Then we will equate the value of the volume of $n$ number of spherical bullets with the volume of the cube of sides $44cm$. After equating the value, we will get the number of spherical bullets that can be made out of a solid cube of lead.

Complete step by step solution:
Let the number of spherical bullets that can be made out of a $44cm$ cube of lead be $n$
Now, let’s find the value of volume of spherical bullets of diameter 4cm and of radius 2cm.
Volume of spherical bullets $=\dfrac{4}{3}\pi {{r}^{3}}$
Now, putting the value of the radius of spherical bullets.
Volume of spherical bullets $=\dfrac{4}{3}\pi {{2}^{3}}$
Simplifying the equation further, we get
$=\dfrac{4}{3}\pi \times 8c{{m}^{3}}$
Now putting the value of pi.
$=\dfrac{4}{3}\times \dfrac{22}{7}\times 8c{{m}^{3}}$
We will multiply the terms now.
$=33.52c{{m}^{3}}$

So to calculate the volume of n number of spherical bullets of radius $2cm$ we will multiply it with n.
Volume of number of spherical bullets$=n\times 33.52c{{m}^{3}}$ …………..$\left( 1 \right)$
Now, calculate the value of volume of cube of sides $44cm$ $={{\left( 44cm \right)}^{3}}$
$=85184c{{m}^{3}}$ ……………..$\left( 2 \right)$

Now, equating equation $\left( 1 \right)$ with equation $\left( 2 \right)$ we get;
 $85184c{{m}^{3}}=n\times 33.52c{{m}^{3}}$
Now, dividing 85184 by 33.52 we get;
$\Rightarrow n=\dfrac{85184c{{m}^{3}}}{33.52c{{m}^{3}}}$
$=2541.288\approx 2541$

So the required number of spherical bullets that can be made out of a cube of metal is 2541.

Note:
Since we have used volume of a cube, where volume is the measurement of space available in a particular object in cubic units.
We can solve this question by using formula i.e.
$\text{number of spherical bullets formed}=\dfrac{\text{volume of cube}}{\text{volume of one spherical bullet}}$