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 . 

Answer 1

Diameter of the spherical lead shots = 4 cm 
Edge length of the solid cube (a) = 44 cm.
Let n be the number of spherical lead shots made out of the solid cube.

\[n \times \text { Volume of the spherical lead shots = Volume of the solid cube }\]

\[ \Rightarrow \frac{\text { Volume of the solid cube }}{\text { Volume of the spherical lead shots }} = n\]

\[ \Rightarrow \frac{a^3}{\frac{4}{3} \pi r^3} = n\]

\[ \Rightarrow \frac{{44}^3}{\frac{4}{3}\pi \times \left( \frac{4}{2} \right)^3} = n\]

\[ \Rightarrow 2541 = n\]

Hence, 2541 spherical lead shots can be made