Find the volume specified. Use 3.14 as the approximate value of , and round your answer to the nearest tenth.
Find the volume of a feed bin having the shape of a right circular cylinder of radius 4 ft and height 8 ft topped by a right circular cone of the same radius and height 8 ft.
To find the volume of the feed bin, we first need to find the volume of the cylinder and the volume of the cone, and then add them together.
The volume of a cylinder is given by the formula V = πr^2h, where r is the radius and h is the height.
For the cylinder, we have:
V_cylinder = π(4 ft)^2(8 ft)
V_cylinder = 3.14(16 ft^2)(8 ft)
V_cylinder = 401.92 ft^3
The volume of a cone is given by the formula V = (1/3)πr^2h.
For the cone, we have:
V_cone = (1/3)π(4 ft)^2(8 ft)
V_cone = (1/3)3.14(16 ft^2)(8 ft)
V_cone = 134.19 ft^3
Now, we can find the total volume by adding the volumes of the cylinder and the cone:
V_total = V_cylinder + V_cone
V_total = 401.92 ft^3 + 134.19 ft^3
V_total = 536.11 ft^3
Therefore, the volume of the feed bin is approximately 536.1 ft^3.