Find the height of the building, Mathematics

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A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains   41(19/21-) cu m of air. If the internal diameter of the building is equal to its total height above the floor, find the height of the building.

( Ans : 4m)

Ans:    Volume of building = 41 (19/21) m3

=> π.r2.r + 2/3 π r3 = 41(19/21)

=> π × r3  × 5/3 = 880/21

 

=> r 3 =  880/21 x 7/22 x 3/5

=> r3 = 8

=> r = 2 m

∴ height of building = 4 cm


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