A dome of a building is in the form of a hemisphere. From inside, it was white- washed at the cost of Rs. 538.89. if the cost of white-washing is Rs. 4.00 per Square meter, Find the
✴ Inside surface area of the dome
✴ Volume of the air inside the dome.
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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
(i) inside surface area of the dome
(ii) volume of the air inside the dome.
Medium
Solution
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(i) We know that
Area whitewashed × Cost of white wash = Total cost
Area whitewashed ×2=498.96
Area whitewashed =
2
498.96
Area whitewashed =249.48 m
2
Now,
Area of whitewashed is curved surface area of hemisphere (as only walls are whitewashed, not floor)
Therefore,
Inner surface area of dome =249.48 m
2
(ii) Volume of air inside dome = Volume of hemisphere
=
3
2
πr
3
Let the radius of dome be 'r' m
Surface area of dome =249.48 m
2
2πr
2
=249.48
2×
7
22
×r
2
=249.48
r
2
=39.69
r=
39.69
r=6.3 m
Volume of air inside the dome = Volume of hemisphere
=
3
2
πr
3
=
3
2
×
7
22
×6.3
3
=523.9 m
3