Question

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. 

Answer 1

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.