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Probability

Question

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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 र 498.96. If the cost of white-washing is र2.00 per square metre, find the
(i) inside surface area of the dome,
(ii) volume of the air inside the dome.

Solution

(i) Inside surface area of the dome

equals fraction numerator 498.96 over denominator 2 end fraction equals 249.48 space straight m squared

(ii) Let the radius of the hemisphere be r m. Inside surface area = 249.48 m² ⇒ 2πr²= 249.48

rightwards double arrow space space 2 cross times 22 over 7 cross times straight r squared equals 249.48 rightwards double arrow space space space space space space space space space straight r squared equals fraction numerator 249.48 cross times 7 over denominator 2 cross times 22 end fraction rightwards double arrow space space space space space space space space straight r squared equals 39.69 space rightwards double arrow space space space space space space space space straight r space equals square root of 39.69 end root rightwards double arrow space space space space space space space space straight r space equals space 6.3 space straight m

therefore

Volume of the air inside the dome =

2 over 3 πr cubed

equals 2 over 3 cross times 22 over 7 cross times left parenthesis 6.3 right parenthesis equals 523.9 space straight m cubed space left parenthesis approx. right parenthesis

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