Chapter 12.5, Problem 36HP

To determine

To determine and justify whether the given statement is always, sometimes, never true.

Answer to Problem 36HP

Never true

Explanation of Solution

Given:

The volume of a cone with radius $r$ and height $h$ equals the volume of a prism with height $h$ .

Formula used:

Volume of cone $=\frac{1}{3}Bh$ , where $B$ is the base area and $h$ is the height of the cone.

Volume of prism $=Bh$ , where $B$ the triangular area and $h$ is the length of the prism.

Explanation:

The volume of a cone with radius $r$ and height $h$ equals the volume of a prism with height $h$ .

The volume of cone will always be less than the volume of prism.

Since, in the formula of cone contains $\frac{1}{3}$ in it, so volume will always be less when compared to prism.

Conclusion:

Therefore, the volume of cone will always be less than the volume of prism.

Hence, the statement is never true.