Question

There are two right circular cones of equal height. The radius of base of one cone is half of the radius of the other. Find the ratio of their volume.​

Answer 1

Answer:

9:25

Step-by-step explanation:

Let r

1

and r

2

be the radii of two cones and V

1

and V

2

be their volumes. Let h be the height of the two cones . Then,

V

1

=

3

1

πr

1

2

h and V

2

=

3

1

πr

2

2

h

Therefore,

V

2

V

1

=

r

2

2

r

1

2

=

25

9

Hence, the ratio of the volumes of two cones is 9 : 25.

Answer 2

Answer:

Let r

1

and r

2

be the radii of two cones and V

1

and V

2

be their volumes. Let h be the height of the two cones . Then,

V

1

=

3

1

πr

1

2

h and V

2

=

3

1

πr

2

2

h

Therefore,

V

2

V

1

=

r

2

2

r

1

2

=

25

9

Hence, the ratio of the volumes of two cones is 9 : 25.