#### 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 Rs 2.00 per square meter, find the

(i) inside surface area of the dome,

(ii) volume of the air inside the dome.

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

#### Solution

(i) Cost of white-washing the dome from inside = Rs 498.96

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

Therefore, CSA of the inner side of dome = (498.96/2) m^{2} = 249.48 m^{2}

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

CSA of inner side of dome = 249.48 m^{2}

2π*r*^{2} = 249.48 m^{2}

`rArr2xx22/7 xxr^2=249.48 m^2`

`rArr r^2=((249.48xx7)/(2xx22))m^2 = 39.69 m^2`

⇒ *r* = 6.3 m

Volume of air inside the dome = Volume of hemispherical dome

`=2/3pir^3`

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

= 523.908 m^{3}

= 523.9 m^{3} (approximately)

Therefore, the volume of air inside the dome is 523.9 m^{3}.