What is the total volume of the shape below if the height of the cylinder is
10
10 inches, the radius of the cylinder is
6
6 inches and the height of the cone is
12
12 inches. Use 3.14 for π.
To find the total volume of the shape, we need to calculate the volumes of the cylinder and cone separately and then add them together.
The volume of a cylinder is given by the formula: V_cylinder = πr^2*h_cylinder
where r is the radius of the cylinder and h_cylinder is the height of the cylinder.
Substitute the given values: V_cylinder = 3.14 * 6^2 * 10
V_cylinder = 3.14 * 36 * 10
V_cylinder = 1130.4 cubic inches
The volume of a cone is given by the formula: V_cone = 1/3 * πr^2 * h_cone
where r is the radius of the cone and h_cone is the height of the cone.
Substitute the given values: V_cone = 1/3 * 3.14 * 6^2 * 12
V_cone = 1/3 * 3.14 * 36 * 12
V_cone = 452.16 cubic inches
Therefore, the total volume of the shape is V_total = V_cylinder + V_cone
V_total = 1130.4 + 452.16
V_total = 1582.56 cubic inches
So, the total volume of the shape is 1582.56 cubic inches.