Question

the diameter of two cylinders are in the ratio of 2:3. find the ratio of their heights if their volumes are equal

Answer 1

Answer:

9:4

Step-by-step explanation:

Let the radius be 2x and 3x

now put it in the formula

equate them you will get

2π*4x^2*h=2π*9x^2*h"

now H/H"=9/4

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Answer 2

The ratio of their heights if their volumes are equal is 6:7

Step-by-step explanation:

The diameter of two cylinders are in the ratio of 2:3.

Let the ratio be x

Diameter 1 = 2x

Radius 1 = $\frac{2x}{2}=x$

Volume of cylinder 1 = $\pi r^2 h = \pi (x)^2 h$

Diameter 2 = 3x

Radius 2 =$\frac{3x}{2}=1.5x$

Volume of cylinder 2 $= \pi (1.5x)^2H$

We are given that  their volumes are equal

So,$\pi (x)^2 h =\pi (1.5x)^2H$

h=2.25H

$\frac{h}{H}=\frac{225}{100}=\frac{6}{7}$

Hence the ratio of their heights if their volumes are equal is 6:7

#Learn more:

The ratio of the radii of two cylinders of equal heights is 1:3.Find the ratio of their volume​

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