Find the volume of the space between the cylinder and the cone. Note the cone is touching the top of the cylinder. The height of the cylinder is 13 inches and the diameter is 60 inches.

Volume of cylinder = πr^2h

Radius of cylinder = diameter/2 = 60/2 = 30 inches
Volume of cylinder = π(30)^2(13) = 11,706π cubic inches

Volume of cone = 1/3πr^2h
Radius of cone = 30 inches
Height of cone = 13 inches
Volume of cone = 1/3π(30)^2(13) = 3,140π cubic inches

Volume of space between cylinder and cone = Volume of cylinder - Volume of cone
= 11,706π - 3,140π
= 8,566π

Therefore, the volume of space between the cylinder and the cone is 8,566π cubic inches.