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 $Rs.2.00$ per square metre, find the
(i) inside surface area of the dome
(ii) volume of the air inside the dome.

Answer 1

(i) We know that

Area whitewashed $\times$ Cost of white wash $=$ Total cost

Area whitewashed $\times 2=498.96$

Area whitewashed $=\frac{498.96}{2}$

Area whitewashed $=249.48m^2$

Now,

Area of whitewashed is curved surface area of hemisphere (as only walls are whitewashed, not floor)

Therefore,

Inner surface area of dome $=249.48m^2$

(ii) Volume of air inside dome $=$ Volume of hemisphere

$=\frac{2}{3}\pi r^3$

Let the radius of dome be 'r' m

Surface area of dome $=249.48m^2$

$2\pi r^2=249.48$

$2\times \frac{22}{7}\times r^2=249.48$

$r^2=39.69$

$r=\sqrt{39.69}$

$r=6.3m$

Volume of air inside the dome $=$ Volume of hemisphere

$=\frac{2}{3}\pi r^3$

$=\frac{2}{3}\times \frac{22}{7}\times {6.3}^3$

$=523.9m^3$