Question

The radii of two cylinders are in the ratio 2:3 and their heights are in the ratio 5:3 then the ratio of their volumes are

• A. 20:27
• B. 40:50
• C. 20:30
• D. 50:30

Answer 1

The Correct Option is A

To solve the problem, we need to find the ratio of volumes of two cylinders given their radii and heights.

1. Formula for Volume of a Cylinder:
The volume of a cylinder is given by:
$ V = \pi r^2 h $
Where $r$ is the radius and $h$ is the height.

2. Given:
- Ratio of radii = $2 : 3$
- Ratio of heights = $5 : 3$

3. Let the radii and heights be:
- $r_1 = 2$, $h_1 = 5$
- $r_2 = 3$, $h_2 = 3$

4. Calculating Volumes:
$V_1 = \pi (2)^2 \cdot 5 = \pi \cdot 4 \cdot 5 = 20\pi$
$V_2 = \pi (3)^2 \cdot 3 = \pi \cdot 9 \cdot 3 = 27\pi$

5. Finding the Ratio:
$ \frac{V_1}{V_2} = \frac{20\pi}{27\pi} = \frac{20}{27} $

Final Answer:
The ratio of the volumes is $ \mathbf{20 : 27} $.