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A circular hall(big room) has a 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 cubic meter



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Let the inner diameter = D
          inner radius = D/2 = r 
Greatest height = D
height of cylindrical part (h)= D-r = r
radius of cylindrical part = r
area of floor = πr²

volume = volume of cylindrical part + volume of hemispherical part
           = πr²h + 2/3 πr³
           = πr³ + 2/3 πr³

48510= \frac{5}{3}  \pi  r^{3}

⇒   r= \sqrt[3]{ \frac{48510*3}{5 \pi } }  = \sqrt[3]{9269.43} =21m

Area\ of\ floor= \pi  r^{2} = \pi *21^{2}=1386\ m^{2}

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