Question

How many spherical lead shots each $4.2cm$ in diameter can be obtained from a rectangular solid (cuboid) of lead with dimensions $66cm,42cm,21cm$. (Take $\pi =\frac{22}{7}$)

• A. $1500$
• B. $1200$
• C. $1300$
• D. $1600$

Answer 1

The correct option is A $1500$

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

As the diameter of the sphere is $4.2$ cm, its radius $r=2.1$ cm

Volume of a cuboid of length $l$, breadth $b$ and height $h$ $=l\times b\times h$.

Number of lead shots formed $=\frac{\text{Volume of lead cuboid}}{\text{Volume of one lead shot sphere}}$

Hence, number of lead shots formed $=\frac{66\times 42\times 21}{\frac{4}{3}\times \frac{22}{7}\times 2.1\times 2.1\times 2.1}=1500$