A building is in the form of a cylinder surmounted by a hemispherical vaulted dome which contains 17.7 m3 of air and its internal diameter is equal to the height of the crown of the vault above the floor. Find the height of the building.
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Answer:
Let r be the radius of hemisphere and cylinder and height of the cylinder =h
Given :
Volume of air =21880 m3
∴ Diameter of the building =2r
Height of the building (H)= diameter of the building
∴ Height of the cylinder + Radius of hemispherical dome =2r
⇒h+r=2r
⇒h=2r−r
⇒h=r
Volume of air inside the building = Volume of hemispherical portion + Volume of cylindrical potion
412119=32πr3+πr2h
412119=32πr3+πr2(r)
21880=32πr3+πr3
21880=πr3(32+1)
21880=722r3×53
22×5
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