Q.

A dome of a building is in the form of a hemisphere. From inside, it was whitewashed, at the cost of Rs. 498.96. If the cost of whitewashing is Rs. 2.00 per square meter, find the inside surface area of the dome and the volume of the air inside the dome.


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a

Question Image,249.48 m2

b

Question Image,250.48 m2

c

Question Image, 259.48 m2

d

None of these 

answer is A.

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Detailed Solution

Concept- First, we will find them inside the surface of an area of the dome then next we will find the volume of the air inside of the dome. We will use the formula of radius and volume and we will get the answer.
(i)We know that Area whitewashedQuestion ImageCost of whitewash = total cost
Area whitewashed Question ImageArea whitewashed Question ImageArea whitewashed Question ImageTherefore, inside the surface area of the domeQuestion Image(ii)Volume of air inside dome=volume of the hemisphere
Question ImageLet the radius of the dome be r m
The surface area of dome =Question ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageQuestion ImageThe volume of air inside the dome= volume of a hemisphere Question ImageHence, the correct option is 1.
 
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