Question

Select the correct answer from each drop-down menu.

Answer 1

The figures cone Z and cylinder Y have the same volume.

Explanation:

The formula for volume of the cone Z is given by

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

The formula for volume of the cylinder Y is given by

$\mathrm{V}=\pi r^{2} \mathrm{h}$

Since, it is given that Cone Z has the same base area as cylinder Y, but its height is three times the height of cylinder Y.

Thus, substituting $h=3h$ in the formula of volume of the cone Z, we get,

$V=\frac{1}{3} \pi r^{2} (3h)$

Simplifying, we have,

$\mathrm{V}=\pi r^{2} \mathrm{h}$

Hence, the volume of the cone Z = volume of the cylinder Y

Thus, the figures cone Z and cylinder Y have the same volume.