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 metre, find the inside surface area of the dome and volume of the air inside the dome.

Explanation

Surface area of a hemisphere =` 2πr^2`
Volume of a hemisphere = `2/3πr^3`
(i) Inside surface area of the dome = Total cost for whitewashing the dome inside /Rate of whitewashing
⇒`498.96/20 = 249.48 metre sq.`
(ii) Let 'r' be the radius of a hemispherical dome.
Inner surface area of the hemispherical dome =' `2πr^2= 249.48 m²
⇒ r^2= 249.48/2π m^2
⇒ r^2 = 249.48 / (2 × 22/7)
⇒ r^2 = 39.69`
⇒`r = sqrt(39.69)
⇒ r = 6.3 m`
The volume of the air inside the dome will be the same as the volume of hemisphere.
Now the volume of the air inside the dome = `2/3πr^3= 2/3 × 22/7 × 6.3 m × 6.3 m × 6.3 m=523.9m^3`' approx