Question

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed at the cost of ₹4989.60. If the cost of whitewashing is ₹20 per square meter, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome

Answer 1

(i) Cost of whitewashing the dome from inside = Rs 498.96
Cost of white washing 1m2 area = Rs 2
Therefore, CSA of the inner side of dome =$\frac{4989.60}{20}$= 249.48 m2

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(ii) Let the inner radius of the hemispherical dome be r.
CSA of inner side of dome = 249.48 m2
$2\pi r^2$ = 249.48 m2

$⇒$ r2 = $\frac{249.48}{2\pi}$ m2

$⇒$ r2 = 249.48 $÷$ (2 ×$\frac{ 22}{7}$)
$⇒$ r2 = 39.69
$⇒$ r = $\sqrt{39.69}$
$⇒$ r = 6.3 m
Volume of air inside the dome = Volume of hemispherical dome
$=\frac{ 2}{3}\pi$r3

$= \frac{2}{3}$ × $\frac{22}{7}$ × 6.3 m × 6.3 m × 6.3 m
= 523.9 m3 (approximately)
Therefore, the volume of air inside the dome is 523.9 m3 .