CameraIcon
CameraIcon
SearchIcon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

A building is in the form of a cylinder surmounted by a hemi-spherical vaulted dome and contains 411921 m3 of air. If the internal diameter of dome is equal to its total height above the floor , find the height of the building ?

Open in App
Solution

let the total height of the building be H m.

let the radius of the base be r m. Therefore the radius of the hemispherical dome is r m.

Now given that internal diameter = total height
2r=H

Total height of the building = height of the cylinder +radius of the dome
⇒ H = h + r

⇒ 2r = h + r
⇒ r = h

Volume of the air inside the building = volume of the cylinder+ volume of the hemisphere
411921=πr2h+23πr388021=πh2h+23πh388021=πh31+2388021=πh353h=2 m

Hence, height of the building H = 2 × 2 = 4m


flag
Suggest Corrections
thumbs-up
6
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Shape Conversion of Solids
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon