Question

*If the ratio of the heights of two cylinders with equal radius is 3: 5, what is the ratio of their volumes?*​

Answer 1

Answer: 3:5

Explanation:

Volume of cylinder: πr^2h

Let the heights be 3x and 5x, radius be r

πr^2 × 3x : πr^2 × 5x

3x : 5x

3:5

Answer 2

Given:-

• Ratio of their heights is 3 : 5.

• Their radius is equal.

To Find:-

• Ratio of their volumes.

Solution:-

Here, Volume of first cylinder is $V_1 = \pi r^{2} h$

And, Volume of second cylinder is $V_2 = \pi r^{2} h$

Since, It is given that ratio of their heights is 3 : 5 and radius is equal.

Then, $\dfrac{V_1}{V_2} = \dfrac{\pi r^{2} h}{\pi r^{2} h}$

      ⇒ $\dfrac{V_1}{V_2} = \dfrac{\pi r^{2} 3h}{\pi r^{2} 5h}$                          [ ∵ radius is equal and heights are in ratio]

      ⇒ $\dfrac{V_1}{V_2} = \dfrac{3h}{5h}$                       [ πr² is canceled because both are equal ]

      ⇒ $\dfrac{V_1}{V_2} = \dfrac{3}{5}$                         [ h is cancelled because it is equal ]

Hence, Ratio of their volumes is 3 : 5 .

Some Important Terms:-

• T.S.A of cylinder = $2 \pi r ( h + r )$

• C.S.A of cylinder = $2 \pi r h$