Asked by Yes
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 the height of the cone is 6 inches? Use 3.14 for pi.
The total volume is ? Cubic inches.
The total volume is ? Cubic inches.
Answers
Answered by
GPT 3.5
First, we need to calculate the volume of the cylinder and the cone separately, then add them together to get the total volume.
Volume of a cylinder:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 6^2 * 5
V_cylinder = 3.14 * 36 * 5
V_cylinder = 3.14 * 180
V_cylinder = 565.2 cubic inches
Volume of a cone:
V_cone = (1/3) * π * r^2 * h
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
Therefore, the total volume of the shape is 791.28 cubic inches.
Volume of a cylinder:
V_cylinder = π * r^2 * h
V_cylinder = 3.14 * 6^2 * 5
V_cylinder = 3.14 * 36 * 5
V_cylinder = 3.14 * 180
V_cylinder = 565.2 cubic inches
Volume of a cone:
V_cone = (1/3) * π * r^2 * h
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
Therefore, the total volume of the shape is 791.28 cubic inches.