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.

To find the volume between the cylinder and the cone, we first need to find the volume of the cylinder and cone individually.

Volume of cylinder:
V_cylinder = πr^2h
Where r is the radius of the cylinder, and h is the height of the cylinder.

Given that the diameter of the cylinder is 60 inches, the radius (r) would be half of that:
r = 60/2 = 30 inches
h = 13 inches

V_cylinder = π(30)^2(13)
V_cylinder = 11700π cubic inches

Volume of cone:
V_cone = 1/3πr^2h
Where r is the radius of the cone, and h is the height of the cone.

Since the cone is touching the top of the cylinder, the height of the cone would be the same as the height of the cylinder, which is 13 inches. The radius of the cone would be the same as the radius of the cylinder, which is 30 inches.

V_cone = 1/3π(30)^2(13)
V_cone = 3900π cubic inches

Now, to find the volume of the space between the cylinder and the cone, we subtract the volume of the cone from the volume of the cylinder:

Volume of space between cylinder and cone = V_cylinder - V_cone
Volume of space between cylinder and cone = 11700π - 3900π
Volume of space between cylinder and cone = 7800π cubic inches

Therefore, the volume of the space between the cylinder and the cone is 7800π cubic inches.