Question

19 17. A building is in the form of a cylinder surrounded by a hemispherical vaulted dome and contains 41 19/21. of air. If the internal diameter of the building is equal to its total height above the floor. Find the height of building.​

Answer 1

Answer:

4m - height of building

Step-by-step explanation:

Let the total height of 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 air inside the building = volume of the cylinder + volume of hemisphere

=> 41 =

=>$\frac{880}{21}$ = $\pi r^{2} h+\frac{2}{3} \pi h^{3}$

=> h = 2m

Height of the building = 2x2 = 4m

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