Question

If a cylinder and a cone have bases of equal radii and are of equal heights, then their volumes are in the ratio of:

• A. 1 : 2
• B. 2 : 3
• C. 3 : 1
• D. 1 : 4

Hint:

The volume of a cone is one-third of the volume of a cylinder with the same base and height.

Answer 1

The Correct Option is C

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: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] Since the base radius and height of the cylinder and cone are the same, the ratio of their volumes is: \[ \frac{V_{\text{cylinder}}}{V_{\text{cone}}} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h} = 3 \] Thus, the correct answer is option (3), 3:1.