Question

A building is in the form of a cylinder surmounted by a hemispherical dome (see Fig. 12.12). The base diameter of the dome is equal to 2/3 the total height of the building. Find the height of the building, if it contains 1408/21 cu.m of the air ?

PLZ HELP !!!!​

Answer 1

Answer:

6 m

Step-by-step explanation:

Let building height = h.

The base diameter of the dome is equal to 2/3 the total height of the building.

=> 2r = (2/3) * h

=> 2r = 2h/3

=> 6r = 2h

=> r = (h/3)

Let height of cylindrical portion = H m.

So, H = h - (h/3) = (2h/3) m.

It contains (1408/21) cu.m of the air.

Volume of air inside building = 1408/21.

=> (2/3)πr³ + πr²H = 1408/21

=> (2/3)π(h/3)³ + π(h/3)²(2h/3) = 1408/21

=> 8/81 πh³ = 1408/21

=> 8/81 * (22/7) * h³ = 1408/21

=> 176/567 h³ = 1408/21

=> h³ = 798336/3696

=> h³ = 216

=> h = 6

Hence, height of the building = 6 m

#Hope my answer help you!