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:
[tex]V = \frac{1}{3} \pi r^2h[/tex]
where, r is the radius and h is the height of the cone.
Volume of cylinder(V') is given by:
[tex]V' = \pi r'^2h'[/tex]
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;
[tex]\frac{V}{V'} = \frac{ \frac{1}{3} \pi r^2h}{\pi r'^2h'} = \frac{ \frac{1}{3} \pi r'^2h'}{\pi r'^2h'}[/tex]
⇒[tex]\frac{V}{V'} =\frac{1}{3} = 1 : 3[/tex]
Therefore, the ratio of the volume of the cone to the volume of the cylinder is, 1 : 3
