Question

How many spherical lead shots each of diameter 4.2 cm can be obtained from a solid rectangular lead piece with dimension  6cm \[\times\] 42cm \[\times\] 21 cm.

Answer 1

The dimensions of the solid rectangular lead piece is 

\[66 cm \times 42 cm \times 21 cm\].

Diameter of the spherical lead shots = 4.2 cm Let n spherical lead shots be obtained from the rectangular piece. 

\[n \times\text {  volume of spherical lead shot = Volume of the rectangular lead piece}\]

\[ \Rightarrow \frac{\text { Volume of the rectangular lead piece}}{\text { volume of spherical lead shot}} = n\]

\[ \Rightarrow \frac{66 \times 42 \times 21}{\frac{4}{3} \pi r^3} = n\]

\[ \Rightarrow \frac{66 \times 42 \times 21}{\mathit{\frac{4}{3}\pi \left( \frac{4 . 2}{2} \right)^3}} = n\]

\[ \Rightarrow \frac{58212}{38 . 808} = n\]

\[ \Rightarrow n = 1500\]

Hence, 1500 lead shots can be formed. 

DISCLAIMER: There is some error in the question given. Instead of 6 cm, there should be 66 cm. 

The result obtained is by taking 66 cm as the dimensions of the rectangular piece.