A dome of a building is in the form of a hemisphere.From inside it was 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.
Let the radius of the dome be r m.
Then area of washing = 2 * pie * r2
Rate of washing = Rs. 2 per m2
Cost of washing = 2 * ( 2 * pie * r2)
But, it is given to be Rs. 498.96
So, 2 ( 2 * pie * r2 ) = 498.96
or, r = 6.3 m
Inside surface area of the dome = 2 * pie * r2 = 2 * 22/7 * 6.3 * 6.3 = 249.48m2
Volume of air inside it = 2/3 * pie * r3
2/3 * 22/7 * 6.3 * 6.3 * 6.3 = 523.908 m3 = 524m3 ( approx.)
Hope it works !!
(i) Cost of white-washing the dome from inside = Rs 498.96
Cost of white-washing 1 m2 area = Rs 2
Therefore, CSA of the inner side of dome =
= 249.48 m2
(ii) Let the inner radius of the hemispherical dome be r.
CSA of inner side of dome = 249.48 m2
2πr2 = 249.48 m2
⇒ r = 6.3 m
Volume of air inside the dome = Volume of hemispherical dome
= 523.908 m3
= 523.9 m3 (approximately)
Therefore, the volume of air inside the dome is 523.9 m3.