Question

find the ratio of the volumes of a cone and of a cylinder whose base diameter and heights are equal

Answer 1

the volume of cone=
$\frac{1}{3} \pi {r}^{2} h$
volume of cylinder is
$\pi {r}^{2}h$
therefore ratio is
$1 \: ratio \: 3$

Answer 2

Answer:

The ratio of  the volumes of a cone and of a cylinder is $\frac{1}{3}$.

Step-by-step explanation:

It is given that the diameter and heights of cone and cylinder are equal.

Let the height of cone and cylinder be h and the diameter of cone and cylinder be d.

Since both have same diameter, therefore they have same radius r.

The volume of cone is

$V_1=\frac{1}{3}\pi r^2h$

The volume of cylinder is

$V_2=\pi r^2h$

The ratio of  the volumes of a cone and of a cylinder is

$\frac{V_1}{V_2}=\frac{\frac{1}{3}\pi r^2h}{\pi r^2h}=\frac{1}{3}$

Therefore the ratio of  the volumes of a cone and of a cylinder is $\frac{1}{3}$.