Suppose a cylinder and alone share the same radius and the same height, which is twice the radius. Which ratio describes the relationship between the formulas for the volume of a cone to the volume of a cylinder?

Answer 1

The volume of a cone is given by the formula V_cone = (1/3)πr^2h, where r is the radius and h is the height of the cone.

The volume of a cylinder is given by the formula V_cylinder = πr^2h, where r is the radius and h is the height of the cylinder.

In this case, the height of the cylinder is twice the radius, which means h = 2r.

Plugging this value of h into the volume formulas:

V_cone = (1/3)πr^2(2r)
V_cone = (2/3)πr^3

V_cylinder = πr^2(2r)
V_cylinder = 2πr^3

The ratio of the volume of the cone to the volume of the cylinder is given by:

(2/3)πr^3 : 2πr^3

Simplifying this ratio:

(2/3) : 2

The relationship between the formulas for the volume of a cone to the volume of a cylinder is 2:3.