Question

Find the volume of the space between the cylinder and the cone. The height of the cylinder is 13 inches and the diameter is 60 inches. Use 3.14

Answer 1

First, we need to find the radius of the cylinder by dividing the diameter by 2:

Radius = 60 inches / 2 = 30 inches

Next, we need to find the volume of the cylinder using the formula V_cylinder = πr^2h:

V_cylinder = 3.14 x (30 inches)^2 x 13 inches
V_cylinder = 3.14 x 900 square inches x 13 inches
V_cylinder = 35,100 cubic inches

Next, we need to find the volume of the cone. The height of the cone is also 13 inches, and the radius is the same as the cylinder (30 inches).

First, we need to find the slant height of the cone using the Pythagorean theorem:

Slant height = √(30^2 + 13^2) = √(900 + 169) = √1069 ≈ 32.7 inches

Next, we can find the volume of the cone using the formula V_cone = 1/3πr^2h:

V_cone = 1/3 x 3.14 x (30 inches)^2 x 13 inches
V_cone = 1/3 x 3.14 x 900 square inches x 13 inches
V_cone = 11,130 cubic inches

Finally, we can find the volume of the space between the cylinder and the cone by subtracting the volume of the cone from the volume of the cylinder:

Volume = V_cylinder - V_cone
Volume = 35,100 cubic inches - 11,130 cubic inches
Volume = 23,970 cubic inches

Therefore, the volume of the space between the cylinder and the cone is 23,970 cubic inches.