There is a hemispherical roof on the cylindrical room .There is 5236 `m^(3)` air in this room .The inner diameter of the floor is equal to the maximum height of the room. Find the height of room . (Given that `pi`=3.1416)

Explanation

Room is shown in the figure
Let diameter of room =h
Radius =`(h)/(2)`
and , total height =h
Height of hemishperical part =`(h)/(2)`
Height of cylindrical part =`h -(h)/(2)=(4)/(2)`
Now volume of room =volume of cylindrical part + volume of hemispherical part
`V=pi((h)/(2))^(2)(h)/(2)+(2)/(3)pi((h)/(2))^(3)=(pih^(3))/(8)+(pih^(3))/(12)=(3piH^(3)+2pih^(3)+2pih^(3))/(24)=(5pih^(3))/(24)`
Given that , `(5pih^(3))/(24)=5236`
`h^(3)=(5236xx24)/(5pi)=(5236xx24)/(5xx3.1416)=(5236xx24)/(15.7080)=8000=20^(3)`
h=20 cm
Height of room = 20 m