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CBSE - X - Mathematics - Surface Areas and Volumes

A building is in the form of a cylinder surmounted by a hemispherical vaulted dome and contains 880/

Asked by poojathally 10th March 2010, 11:41 AM
Answered by Expert

Answer:

Let R be the radius, and h be the height of the cylindrical portion.

Height of the building, R+h = 2R = D = internal diameter.

This gives, h = R.

Volume = Volume of cylindrical portion + Volume of hemispherical portion

= πR2h + (4πR3/3)/2 = 880/21

(22/7)(R2h + 2R3/3) = 880/21

R2(h+2R/3) = 440/3

R2(R+2R/3) = 440/3

R3(5/3) = 440/3

R3 = 88

R = 4.45 m

and Total Height of the building, = R+h = 2R = 8.9 m

Regards,

Team,

TopperLearning.

 

Answered by Expert 10th March 2010, 2:56 PM

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