Question

How many shots each having diameter of $3cm$ can be made from a cuboidal lead solid of dimensions $9cm\times 11cm\times 12cm$ ?

Answer 1

Given:
Dimensions of cuboid
$=9cm\times 11cm\times 12cm$

$\therefore$ Volume of cuboid
$=9\times 11\times 12=1188c{m}^3$ ($\because \text{Volume~ of~ cuboid}=l\times b\times h)$

Diameter of shot (sphere) $=3cm$
$\therefore$ Radius of shot, $r=\frac{3}{2}=1.5cm$

Volume of shot (Spherical in shape) $=$

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

$=\frac{4}{3}\times \frac{22}{7}\times (1.5{)}^3$

$=\frac{297}{21}=14.143c{m}^3$

$\therefore$ Required number of shots $=\frac{\text{Volume of cuboid}}{\text{Volume of one shot(Sphere)}}=\frac{1188}{14.143}=84$ (approx.)