A cylinder and a cone have the same volume. The Cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches. What is the height of the cone?

Answer 1

A cylinder and a cone have the same volume. The Cylinder has a radius of 2 inches and a height of 3 inches. The cone has a radius of 3 inches. What is the height of the cone?

V_cylinder = V_cone

V_cylinder = πr²h

V_cone = (1/3)πr²h

V_cylinder = V_cone = 12π in³

h_cone = 3V_cone ÷ (πr²)

h_cone = 36π ÷ 9π

h_cone = 4 in