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 R s . 2.00 per square metre, find the(i) inside surface area of the dome
(ii) volume of the air inside the dome.
Submitted on 23/12/2023 | Answered by Vandana Rana
Answer :
(i) We know that
Area whitewashed × Cost of white wash =
Total cost Area whitewashed × 2
=498.96 Area whitewashed =498.96/2
=249.48 m²
Area of whitewashed is curved surface area of hemisphere
Therefore, Inner surface area of dome =249.48 m²
(ii) Volume of air inside dome = Volume of hemisphere=2πr³/3
Let the radius of dome be 'r'
Surface area of dome =249.48m²
2πr² =249.48
2×22/7×r² =249.48
r²=39.69
r = √39.69
r = 6.3 m
Volume of air inside the dome =Volume of hemisphere =(2/3)×πr³
=[ 2×22×(6.3)³]/(7×3)
=523.9 m³