Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of Rs. $498.96$. If the cost of white-washing is Rs. $2$ per square metre, find the inside surface area of the dome and volume of the air inside the dome.

Answer 1

Let r be the inner radius of the hemispherical dome. Then,

Inside surface area = $2\pi r^2$

Cost of white-washing at the rate of Rs. $2$ per m${}^2$ = Rs. $(2\pi r^2\times 2)=Rs.4\pi r^2$

Cost of white-washing $=Rs.\mathrm{498.96.}$

$4\pi r^2=498.96$

$4\times \frac{22}{7}\times r^2=498.96$

$r^2=39.69$

$r=6.3$

Inside surface area of the dome = $2\pi r^2=249.48$ $c{m}^2$

Volume of the dome = $\frac{2}{3}\pi r^3=523.908$ $c{m}^3$