Question

The base radii of two cones are in the ratio 3:5 and their heights are in the ratio 2:3. What

is the ratio of their volumes?​

Answer 1

Step-by-step explanation:

Volume of a cone =

3

1

πr

2

h where r

is the radius of the base of the cone and h is the height.

Since height is the same for the two cones, let r

1

and h

1

be the radius and height of the first cone and r

2

and h

2

be

the radius and height of the second cone.

Now, ratio of their volumes is calculated as:

V

1

:V

2

=

3

1

πr

1

2

h

1

:

3

1

πr

2

2

h

2

=r

1

2

h

1

:r

2

2

h

1

=

r

2

2

r

1

2

:

h

1

h

2

=(

3

2

)

2

:

3

2

=

9

4

:

3

2

=2:3

Hence, their volumes are in the ratio 2:3

Answer 2

Step-by-step explanation:

let radii 3r and 5r and height be 2h and 3h

⅓×π3r×3r×2h:⅓×π×5r×5r×3h

9r×2h:25r×3h

18rh:75rh

6. :. 25