Question

Calculate the volume of the hemispherical dome if the height of the dome is 21m.
( Take π=22/7)
a) 19404 cu.m b) 2000 cu.m c) 15000cu.m d)19000cu.m

Answer 1

Step-by-step explanation:

Given:-

Height of the dome is 21m.

To find:-

Calculate the volume of the hemispherical dome if the height of the dome is 21m. ?

Solution:-

Given that

Height of the hemispherical dome = 21 m.

We know that

Height of the hemispherical dome = Diameter of

the hemispherical dome

h = d

=> h = 2× radius

=> radius = h/2 units

Radius of the hemispherical dome = 21/2 m

We know that

Volume of a hemisphere = (2/3)πr^3 cubic units

Where ,π=22/7

On Substituting these values in the above formula

=> V = (2/3)×(22/7)×(21/2)^3 cubic m

=> V = (2/3)×(22/7)×(21/2)×(21/2)×(21/2)

=> V = (2×22×21×21×21)/(3×7×2×2×2)

=>V = (11×21×21)/2

=> V = 4851/2

=> V = 2425.5 cubic m

Answer:-

Volume of the hemispherical dome is 2425.5 cubic.m

There is no correct option in the given options

Note :-

If the radius of the dome is 21 m then we get 19404 cubic m which is in the given options.

Used formula:-

• Height of the hemispherical dome = Diameter of dome
• Radius of the hemisphere = height/2
• Volume of a hemisphere = (2/3)πr^3 cubic units
• π=22/7

Answer 2

Answer:

Option a) 19404 cu.m.

Step-by-step explanation:

Given: Height of the hemispherical dome = 21m
Height of a hemispherical dome = its radius

Therefore, radius(r) = 21m

V = 2/3πr^3
  = 2/3 * 22/7 * 21 * 21 * 21
  = 19404 cu.m.