Question

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

• A. $525.9m^3$.
• B. $223.9m^3$.
• C. $123.9m^3$.
• D. $523.9m^3$.

Answer 1

The correct option is D

$523.9m^3$.

Cost of whitewashing the dome from inside = Rs. 498.96
Cost of white-washing $1m^2$ area = Rs. 2
Therefore, CSA of the inner side of dome $=\left(\frac{498.96}{2}\right)m^2$
$=249.48m^2$
Let the inner radius of the hemispherical dome be r.
$2\pi r^2=249.48m^2$
$\Rightarrow 2\times \frac{22}{7}\times r^2=249.48m^2$
$\Rightarrow r^2=\left(\frac{249.48\times 7}{2\times 22}\right)$
$\Rightarrow r=6.3m$
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 $523.9m^3$.