What is the total volume of the shape below if the height of the cylinder is 5 inches, the radius of the cylinder is 6 inches and the height of the cone is 6 inches? Use 3.14 for pi.
First, we need to calculate the volumes of the cylinder and the cone separately, then add them together to get the total volume.
1. Volume of the cylinder:
V_cylinder = πr^2h
V_cylinder = 3.14 * 6^2 * 5
V_cylinder = 3.14 * 36 * 5
V_cylinder = 3.14 * 180
V_cylinder = 565.2 cubic inches
2. Volume of the cone:
V_cone = (1/3)πr^2h
V_cone = (1/3) * 3.14 * 6^2 * 6
V_cone = (1/3) * 3.14 * 36 * 6
V_cone = (1/3) * 3.14 * 216
V_cone = 226.08 cubic inches
Total volume:
Total volume = V_cylinder + V_cone
Total volume = 565.2 + 226.08
Total volume = 791.28 cubic inches
So, the total volume of the shape is 791.28 cubic inches.