Question

A cylinder and a cone have congruent heights and radii.what is the ratio of the volume of the cone to the volume of the cylinder?

Answer 1

Cone=(hpr^2)/3, cylinder=hpr^2, so the ratio:

cone:cylinder=1/3:1 or using integers by convention:

cone:cylinder=1:3

Answer 2

Answer:

1: 3 ratio of the volume of the cone to the volume of the cylinder

Step-by-step explanation:

Volume of cone(V) is given by:

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

where, r is the radius and h is the height of the cone.

Volume of cylinder(V') is given by:

$V' = \pi r'^2h'$

where,  r' is the radius and h' is the height of the cylinder.

As per the statement:

A cylinder and a cone have congruent heights and radii.

⇒r = r' and h = h'

then;

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

⇒$\frac{V}{V'} =\frac{1}{3} = 1 : 3$

Therefore, the ratio of the volume of the cone to the volume of the cylinder is, 1 : 3