 # How many spherical lead shots of diameter 4 cm

Question:

How many spherical lead shots of diameter 4 cm can be made out of a solid cube of lead whose edge

measures 44 cm.

Solution:

∴ Number of spherical lead shots

$=\frac{\text { Volume of a soiid cube of lead }}{\text { Volume of a spherical lead shot }}$ ...(i)

Given that, diameter of a spherical lead shot i.e., sphere = 4cm

$\Rightarrow \quad$ Radius of a spherical lead shot $(r)=\frac{4}{2}$

$r=2 \mathrm{~cm}$ $[\because$ diameter $=2 \times$ radius $]$

So, volume of a spherical lead shot i.e., sphere

$=\frac{4}{3} \pi r^{3}$

$=\frac{4}{3} \times \frac{22}{7} \times(2)^{3}$

$=\frac{4 \times 22 \times 8}{21} \mathrm{~cm}^{3}$

Now, since edge of a solid cube $(a)=44 \mathrm{~cm}$

So, volume of a solid cube $=(a)^{3}=(44)^{3}=44 \times 44 \times 44 \mathrm{~cm}^{3}$

From Eq. (i),

Number of spherical lead shots $=\frac{44 \times 44 \times 44}{4 \times 22 \times 8} \times 21$

$=11 \times 21 \times 11=121 \times 21$

$=2541$

Hence, the required number of spherical lead shots is 2541.