Question

An iron pillar consists of a cylindrical portion $2.8m$ high and $20cm$ in diameter and a cone $42cm$ high is surmounting it. Find the weight of the pillar, given that $1c{m}^3$ of iron weight $7.5g$

Answer 1

It is given that
Height of the cylinder $=2.8m=280cm$
Diameter of the cylinder $=20cm$
Radius of the cylinder $=20/2=10cm$
Height of the cone $=42cm$

We know that

Volume of the pillar $=\pi r^{2}h+\frac{1}{3}\pi r^{2}H$

It can be written as

Volume of the pillar $=\pi r^2(h+\frac{1}{3}H)$

By substituting the values

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

On further calculation

Volume of the pillar $=\frac{2200}{7}\times (280+14)=92400c{m}^3$

So the weight of pillar $=\frac{(92400\times 7.5)}{1000}=693kg$

Therefore, the weight of the pillar is $693kg$