The volume of a cylinder is represented below V=27π cm3 What would be the volume of a cone that has the same height and diameter as the cylinder? (1 point) Responses V=81π cm3 V=81π cm3 V=3π cm3 V=3π cm3 V=18π cm3 V=18π cm3 V=9π cm3

Answer 1

The volume of a cylinder is given by the formula:

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

The volume of a cone is given by the formula:

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

Since the cone has the same height $h$ and diameter (and thus radius $r$) as the cylinder, the volume of the cone would be one third of the cylinder's volume.

Given that the volume of the cylinder is $V_{cylinder}=27\pi ,{\text{cm}}^3$, we can find the volume of the cone:

$$V_{cone}=\frac{1}{3}{V}_{cylinder}=\frac{1}{3}(27\pi )=9\pi ,{\text{cm}}^3$$

Therefore, the volume of the cone is:

$$\boxed{{\displaystyle 9\pi ,{\text{cm}}^3}}$$