Question

A circular hall(big room) has hemispherical roof. The greatest height is equal to the inner diameter.Find the area of the floor given that the capacity of the hall is 48510 m3.

Answer 1

let radius of the hall = r
As per question= Volume of cylindrical Hall + Volume of dome
                        = πr²*r+ (4/3) πr³/2
                        = πr³ + 2πr³/3 =5πr³/3
then we have    5πr³/3=48510
                              r³=9264.72
                         ⇒  r=21.0028
       Area of floor= πr²=π*441.118=1385.81
                         Floor area is 1385 m²

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