Question

a building is in the form of cylinder surmounted by a hemispherical dome . the base diameter of the dome is equal to 2/3of the total height of building . find the height of the building if it contain 67*1/21 cm square of air

Answer 1

Answer:

The height of the building is 6 cm

Step-by-step explanation:

Let the radius of the cylinder = radius of the hemisphere = r

Let the height of the cylinder = h

Total height of the structure = h + r

From the given condition,

d = 2(h+r)/3

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

=> r = (h+r)/3

=> 3r = h+r

=> h = 2r

Total volume of the air

= volume of cylinder + volume of dome = 67 1/21 = 1408/21

=> πr²h + 2πr³/3 = 1408/21

=> πr²(2r) + 2πr³/3 = 1408/21

=> 8πr³/3 = 1408/21

=> r³ = (1408 x 3 x 7)/(8 x 22 x 21)

=> r³ = 8

=> r = 2 cm

=> h = 2r = 4

Hence height of the building = h + r = 4 + 2 = 6 cm

Answer 2

Answer:

Step-by-step explanation:

Please refer the attachment below

Thank you...