​If the base of a cylinder is the same as that of a cone, and the height of the cylinder is also the same as that of the cone, then find the ratio of the volumes of the cylinder and the cone.

Correct option is D

Given:

The base of the cylinder and cone are the same, so their radii (r) are equal.

The height (h) of the cylinder and cone are also the same.

Formula Used:
The formula for the volume of a cylinder is:

​$$V_{\text{cylinder}} = \pi r^2 h$$​​

The formula for the volume of a cone is:

​$$V_{\text{cone}} = \frac{1}{3} \pi r^2 h$$​​

The ratio of their volumes is:

​$$\text{Ratio} = \frac{V_{\text{cylinder}}}{V_{\text{cone}}}.$$​​

Solution:

Substitute the formulas:

​$$\text{Ratio} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h}$$​​

​$$\text{Ratio} = \frac{1}{\frac{1}{3}} = 3$$

Option (d) is right.