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 $41\frac{19}{21}{\mathrm{m}}^{3}$ 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 $⇒41\frac{19}{21}={\mathrm{\pi r}}^{2}\mathrm{h}+\frac{2}{3}{\mathrm{\pi r}}^{3}\phantom{\rule{0ex}{0ex}}⇒\frac{880}{21}={\mathrm{\pi h}}^{2}\mathrm{h}+\frac{2}{3}{\mathrm{\pi h}}^{3}\phantom{\rule{0ex}{0ex}}⇒\frac{880}{21}={\mathrm{\pi h}}^{3}\left(1+\frac{2}{3}\right)\phantom{\rule{0ex}{0ex}}⇒\frac{880}{21}={\mathrm{\pi h}}^{3}\left(\frac{5}{3}\right)\phantom{\rule{0ex}{0ex}}⇒\mathrm{h}=2\mathrm{m}$ Hence, height of the building H = 2 × 2 = 4m

Suggest Corrections
6
Join BYJU'S Learning Program
Related Videos
Shape Conversion of Solids
MATHEMATICS
Watch in App
Explore more
Join BYJU'S Learning Program