#### 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 R s . 2.00 per square metre, find the(i) inside surface area of the dome

(ii) volume of the air inside the dome.Submitted on 23/12/2023 | Answered by Vandana Rana

#### Answer :

(i) We know that```
Area whitewashed × Cost of white wash =
```

Total cost Area whitewashed × 2

=498.96 Area whitewashed =498.96/2

=249.48 m²

Area of whitewashed is curved surface area of hemisphereTherefore, Inner surface area of dome =249.48 m²

(ii) Volume of air inside dome = Volume of hemisphere=2πr³/3

Let the radius of dome be 'r'

```
Surface area of dome =249.48m²
```

2πr² =249.48

2×22/7×r² =249.48

r²=39.69

r = √39.69

r = 6.3 m

Volume of air inside the dome =Volume of hemisphere =(2/3)×πr³

=[ 2×22×(6.3)³]/(7×3)

=523.9 m³