Question

The ratio of volumes of two cones is 4:5 and the ratio of their radii is 2:3. Find the ratio of their heights.​

Answer 1

Answer:

We have,

V

1

:V

2

=4:5 and r

1

:r

2

=2:3

Let the radius and height of first cone be r

1

and h

1

respectively and of second cone be r

2

and h

2

respectively.

∴

V

2

V

1

=

5

4

⇒

3

1

πr

2

2

h

2

3

1

πr

1

2

h

1

=

5

4

⇒

9h

2

4h

1

=

5

4

⇒

h

2

h

1

=

5

9

.