Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of $498.96$. If the cost of white-washing is $2.00$ per square metre, find
(i) the inside surface area of the dome and
(ii) volume of the air inside the dome.

Answer 1

Given:

Cost of white washing dome $=498.96$

Cost of white washing $1$m${}^2$ area $=$ Rs.$2$

(i) CSA$=\frac{498.96}{2}=249.48$m${}^2$

(ii) Let ratio $=r$, CSA $=249.48m^2$

$\Rightarrow$$249.48=2\times \frac{22}{7}\times r^2$........$\left(2\pi r^2\right)$

$\Rightarrow$$r^2=\frac{249.48\times 7}{44}=39.7$m${}^2$

$\Rightarrow$$r=6.3$ m

Volume of air inside dome $=$ Vol of hemispherical dome

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

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

$=523.9$ m${}^3$