Question

if the ratio of the volume of two cones is 2:3 and the ratio of their radii of their bases is 1:2 then find the ratio of their height

Answer 1

The answer is 8:3 . Mark me brainliest.

Answer 2

The ratio of their heights is 8:3

Step-by-step explanation:

Ratio of volume of two cones is 2:3

Let the ratio be x

So, Volumes of two cones are 2x and 3x

The ratio of their radii of their bases is 1:2

Let the ratio be y

So, Radii of their bases are y and 2y

Let the height be h and H

So, Volume of cone 1 =$\pi r^2 h = \pi y^2 h=2x$

$\Rightarrow h=\frac{2x}{\pi y^2}$

So, volume of cone 2 =$\pi r^2 h = \pi (2y)^2 H=3x$

$\Rightarrow H=\frac{3x}{\pi 4y^2}$

So, Ratio of heights =$\frac{\frac{2x}{\pi y^2}}{\frac{3x}{\pi 4y^2}}=\frac{8}{3}$

So, the ratio of their heights is 8:3

#Learn more:

The radii of the bases of a cylinder and a cone are in the ratio of 3:4 and their heights are in the ratio 2:3.Find the ratio of their volumes.

https://brainly.in/question/9910