Question

A cylinder and a cone have bases of equal radii and heights, then the ratio of volumes is:

• A. 3:1
• B. 2:1
• C. 1:1
• D. 4:1

Hint:

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

Answer 1

The Correct Option is A

The volume of a cylinder is given by the formula: \[ V_{\text{cylinder}} = \pi r^2 h \] The volume of a cone is given by the formula: \[ V_{\text{cone}} = \frac{1}{3} \pi r^2 h \] Since both the cylinder and cone have the same radius \( r \) and height \( h \), the ratio of their volumes is: \[ \frac{V_{\text{cylinder}}}{V_{\text{cone}}} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h} = 3:1 \] Thus, the ratio of the volumes of the cylinder and cone is \( 3:1 \).