A right circular cylinder with a height of 20 cm and a right circular cone share a circular base and have the same volume. What is the height of the cone?

Cone V = 1/3π(r^2)h

Cylinder V = π(r^2)h

1/3π(r^2)h = π(r^2)h

Dividing both sides by π(r^2) and inserting value for h:

1/3h = 20

h = ?

20

To find the height of the cone, we need to compare the volumes of the cylinder and the cone and set them equal to each other.

The volume of a right circular cylinder is given by the formula:
V_cylinder = π * r^2 * h_cylinder

where r is the radius of the circular base and h_cylinder is the height of the cylinder.

The volume of a right circular cone is given by the formula:
V_cone = (1/3) * π * r^2 * h_cone

where r is the radius of the circular base and h_cone is the height of the cone.

Given that the height of the cylinder is 20 cm, we can set up the equation:

π * r^2 * 20 = (1/3) * π * r^2 * h_cone

The π * r^2 terms are common to both sides of the equation and can be canceled out:

20 = (1/3) * h_cone

Multiply both sides of the equation by 3:

60 = h_cone

Therefore, the height of the cone is 60 cm.