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 volume of the air inside the dome.

Answer 1

Let the radius of dome $=r$

Then, we know that

Surface area of dome $=2\pi r^2$ (because it is hemisphere)

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

$r^2=\frac{249.48\times 7}{44}$

$r^2=39.69$

$r=\sqrt{39.69}$

$r=6.3m$

Again, we know that

Volume of hemisphere= volume of air inside the dome

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

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

$=523.908m^3(approx.)$

Hence, this is the answer.