Question

Question 8 (ii)
A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹ 498.96. If the cost of whitewashing is ₹ 2 per square meter, find the:
volume of the air inside the dome
$[Assume\pi =\frac{22}{7}]$

Answer 1

(ii) Cost of whitewashing the dome from inside = ₹. 498.96
Cost of white-washing $1m^2$ area = ₹ 2

Therefore, CSA of the inner side of dome =$\frac{totalcost}{costof1m^2}$ $=\left(\frac{498.96}{2}\right)m^2$
$=249.48m^2$

Let the inner radius of the hemispherical dome be r.
$2\pi r^2=249.48m^2$ [CSA of hemisphere $2\pi r^2$]
$\Rightarrow 2\times \frac{22}{7}\times r^2=249.48m^2$
$\Rightarrow r^2=\left(\frac{249.48\times 7}{2\times 22}\right)$
$\Rightarrow r=6.3m$

Volume of air inside the dome = Volume of hemispherical dome
$=\frac{2}{3}\pi r^3=[\frac{2}{3}\times \frac{22}{7}\times (6.3{)}^3]m^3=523.908m^3=523.9m^3\left(approximately\right)$

Therefore, the volume of air inside the dome is $523.9m^3$.