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.
(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 = (498.96/2) m2 = 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
`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
= 523.908 m3
= 523.9 m3 (approximately)
Therefore, the volume of air inside the dome is 523.9 m3.
Video Tutorials For All Subjects
- Volume of a Sphere