Question:
An iron pillar consists of a cylindrical portion 2.8 m high and 20 cm in diameter and a cone 42 cm high is surmounting it. Find the weight of the pillar, given that 1 cubic cm of iron weighs 7.5 gm.
Solution:
Volume of cylindrical portion
$=\pi r^{2} h$
$=\frac{22}{7} \times\left(\frac{20}{2}\right)^{2} \times 280$
$=88000 \mathrm{~cm}^{3}$
Volume of conical portion
$=\frac{1}{3} \pi r^{2} h$
$=\frac{1}{3} \times \frac{22}{7} \times(10)^{2} \times 42$
$=4400 \mathrm{~cm}^{3}$
Total number
$=8800+4400$
$=92400$
So total height
$=92400 \times 7.5$
$=693000 \mathrm{gm}$
$=693 \mathrm{~kg} .$