What is the total volume of the shape below if the height of the cylinder is
9
9 inches, the radius of the cylinder is
5
5 inches and the height of the cone is
21
21 inches. Use 3.14 for π
First, we need to calculate the volume of the cylinder. The formula for the volume of a cylinder is:
V_cylinder = π * r^2 * h
Where r is the radius and h is the height of the cylinder.
Given:
r = 5 inches
h = 9 inches
V_cylinder = 3.14 * 5^2 * 9
V_cylinder = 3.14 * 25 * 9
V_cylinder = 3.14 * 225
V_cylinder = 706.5 cubic inches
Next, we need to calculate the volume of the cone. The formula for the volume of a cone is:
V_cone = (1/3) * π * r^2 * h
Where r is the radius and h is the height of the cone.
Given:
r = 5 inches
h = 21 inches
V_cone = (1/3) * 3.14 * 5^2 * 21
V_cone = (1/3) * 3.14 * 25 * 21
V_cone = (1/3) * 3.14 * 525
V_cone = 549.5 cubic inches
Finally, to find the total volume, we add the volumes of the cylinder and the cone:
Total volume = V_cylinder + V_cone
Total volume = 706.5 + 549.5
Total volume = 1256 cubic inches
Therefore, the total volume of the shape is 1256 cubic inches.