Question

 A cone and a hemisphere have equal bases and equal heights. The ratio of their volumes is : *


a 3 : 1
b 1 : 2
c √2 : 1
d None of the above


​

Answer 1

Step-by-step explanation:

Let the radius of base of hemisphere and cone, each be r unit.

Let the height of the cone be h unit.

Volume of the cone=

3

1

πr

2

h

Volume of the hemisphere =

3

2

πr

3

According to the question.

3

1

πr

2

h=

3

2

πr

3

⇒h=2r

⇒ Height of the cone =2r unit

Height of the hemisphere = Radius of the hemisphere =r

∴ Ratio of the heights of cone and hemisphere =2r:r=2:1

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