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प्रश्न
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
- inside surface area of the dome,
- volume of the air inside the dome.
`["Assume "pi=22/7]`
उत्तर
(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.
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