# 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.

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 cm3 of iron weights 7.5 g.

Solution:

Height of the cylindrical portion of the iron pillar, = 2.8 m = 280 cm
Radius of the cylindrical portion of the iron pillar, r = 20 cm
Height of the cone which is surmounted on the cylindrical portion, H = 42 cm
Now, volume of the pillar = volume of the cylindrical portion + volume of the conical portion

$=\pi r^{2} h+\frac{1}{3} \pi r^{2} H$

$=\frac{22}{7} \times 10^{2}\left(280+\frac{1}{3} \times 42\right)$

$=\frac{22}{7} \times(280+14)$

$=\frac{22}{7} \times 100 \times 294$

$=92400 \mathrm{~cm}^{3}$

$\therefore$ Weight of the pillar = volume of the pillar $\times$ weight per cubic $\mathrm{cm}$

$=92400 \times \frac{7.5}{1000}$

$=693 \mathrm{~kg}$