Question

THE radii of two cones are in ratio 2:3 and their volume in the ratio 1:3.what is the ratio of their heights?

Answer 1

Answer:

Step-by-step explanation:

Volume of a cone =31​πr2h 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 r1​ and h1​

be the radius and height of the first cone and r2​ and h2​ be

the radius and height of the second cone.

Now, ratio of their volumes is calculated as:

V1​:V2​

=31​πr1​2h1​:31​πr2​2h2​

=r1​2h1​:r2​2h1​

=r2​2r1​2​:h1​h2​​

=(32​)2:32​

=94​:32​

=2:3

Hence, their volumes are in the ratio 2:3