Question

A dome of a building is in the form of a hemisphere. From inside, it was white-washed at the cost of ₹ 4989.60 If the cost of white-washing is ₹ 20 per square meter, find the

1. inside surface area of the dome,
2. volume of the air inside the dome.

`["Assume "pi=22/7]`

Answer 1

(i) Cost of white-washing the dome from inside = ₹ 4989.60

Cost of white-washing 1 m² area = ₹ 20

Therefore, the curved surface area of the inner side of the dome =  `(4989.60/20) m^2` = 249.48 m²

(ii) Let the inner radius of the hemispherical dome be r.

Curved surface area of the inner side of the dome = 249.48 m²

2πr² = 249.48 m²

⇒ `2xx22/7 xxr^2=249.48  m^2`

⇒ r² = `((249.48xx7)/(2xx22))m^2` = 39.69 m²

⇒ r = 6.3 m

The volume of air inside the dome = Volume of the hemispherical dome

= `2/3pir^3`

= `[2/3xx22/7xx(6.3)^3]m^3`

= 523.908 m³

= 523.9 m³     (approximately)

Therefore, the volume of air inside the dome is 523.9 m³.