Question

A building is in the form of cylinder surmounted by a hemispherical dome. The base diameter of the dome is equal to 23 of the total height of the building. Find the height of the building if it contains 67121m3 of air.

Open in App
Solution

Height of building = height of cylinder + height of hemisphereH=h+rr is radius of cylinder and domediameter of dome =2/3× height of building∴2r=23×(h+r)∴6r=2h+2r ∴3r=h+r∴h=2rVolume of air in building = Volume of cylinder+ Volume of dome∴67121=πr2h+23πr3∴140821=πr2(h+23r)=πr2(2r+2/3r)=πr2(83r)∴140821=83πr3∴14087=8×227×r3∴r3=140822×8=8∴r=2 m⇒h=4 mHeight of building =r+h=6 m

Suggest Corrections
5
Related Videos
Combination of Solids
MATHEMATICS
Watch in App
Explore more