Question

A cone and a hemisphere have equal basis and equal volume . Find the ratio of their heights​

Answer 1

Answer:

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

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