A cylindrical hall has a hemispherical roof. The maximum height of the hall is equal to the base diameter. If the total volume of the hall is 7546/3 m cube, find the total inner surface area of the hall.
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A cylindrical hall has a hemispherical roof. The maximum height of the hall is equal to the base diameter. If the total volume of the hall is 7546/3 m cube, find the total inner surface area of the hall.
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ANSWER....
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