The radius of the base of the cylinder is 6 and the radius of the base of the cone is 9. The generatrix of the cylinder

The radius of the base of the cylinder is 6 and the radius of the base of the cone is 9. The generatrix of the cylinder is equal to the height of the cone. Find the ratio of the volume of the cone to the volume of the cylinder.

The volume of a cylinder is equal to the product of the radius of the base squared by the number Pi and the height:

Vts = πr ^ 2h;

Vts = 6 ^ 2 π h = 36πh.

The volume of the cone is equal to one third of the product of the square of the base radius by the height and by the PI number:

Vk = 1/3 π r ^ 2 h;

Vк = 1/3 π 9 ^ 2 h = 81/3 π h = 27πh.

Now we find the ratio of the volumes of the cylinder and the cone:

Vts: Vk = 36πh / 27πh = 36/27 = 4/3.

Answer: The ratio of the volume of the cylinder to the volume of the cone is 4/3.