A cylinder and a cone have congruent bases and the same volume. What could be the height of the cylinder and the height of the cone? A height of cylinder = 4 cm height of cone = 12 cm B height of cylinder = 12 cm height of cone = 3 cm C height of cylinder = 12 cm height of cone = 16 cm D height of cylinder = 36 cm height of cone = 12 cm

Step-by-step explanation:

The volume of a cylinder is expressed as

V = πr^2h

Where

π is a constant

h is the height of the cylinder

The volume of a cone is expressed as

V = 1/3πr^2h

Where

π is a constant

h is the height of the cone

If the cylinder and a cone have congruent bases and the same volume, it means that

πr^2h = 1/3πr^2h

πr^2 cancels out on both the left hand side and right hand side of the equation. It becomes

h = h/3

It means that the height of the cone is 3 times the height of the cylinder. Therefore,

If height of cylinder = 4 cm, height of cone = 12 cm