Question

A cylinder and a right circular cone are having the same base and same height.

The volume of the cylinder is _______ the volume of the cone.

• A. three times
• B. four times
• C. half
• D. None of these

Answer 1

The correct option is A

three times

Step 1: Given data

Since a cylinder and a right circular cone are having the same base and same height

Radius of cylinder and cone$=r$

Height of cylinder and cone$=h$

Volume of cone$=\frac{1}{3}{\mathrm{\pi r}}^{2}h$

Volume of cylinder$={\mathrm{\pi r}}^2\mathrm{h}$

Step 3: Calculating the relation between the volume of cone and volume of a cylinder

As per the given data,

The volume of cone$=\frac{1}{3}{\mathrm{\pi r}}^2\mathrm{h}=\frac{1}{3}\times$Volume of the cylinder

Thus, the Volume of the cylinder$=3\times$Volume of cone

Hence, option A is correct.