A cylinder has a cone on top. The base of the cone is congruent to the base of the cylinder. The diameter of the base is 16ft. The height of the cylinder is 16ft. and the height of the cone is 9th. What is the volumeof the entire figure?
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To find the volume of the entire figure, we 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_cylinder = π * r^2 * h, where r is the radius of the base and h is the height. In this case, the diameter of the base is given as 16ft, so the radius is half of that, which is 8ft. The height of the cylinder is given as 16ft. Plugging in these values, we get:
V_cylinder = π * (8ft)^2 * 16ft
The volume of a cone is given by the formula V_cone = (1/3) * π * r^2 * h, where r is the radius of the base and h is the height. Since the base of the cone is congruent to the base of the cylinder, the radius of the cone is also 8ft. The height of the cone is given as 9ft. Plugging in these values, we get:
V_cone = (1/3) * π * (8ft)^2 * 9ft
Now we can add the volume of the cylinder and the volume of the cone to get the total volume of the figure:
V_total = V_cylinder + V_cone
Simplifying this equation, we have:
V_total = π * (8ft)^2 * 16ft + (1/3) * π * (8ft)^2 * 9ft
V_total = π * (8ft)^2 * (16ft + (1/3) * 9ft)
V_total = π * (8ft)^2 * (16ft + 3ft)
V_total = π * (8ft)^2 * 19ft
Now we can use a calculator to find the value of this expression. Using the value of π as approximately 3.14159, we can calculate:
V_total ≈ 3.14159 * (8ft)^2 * 19ft
V_total ≈ 3.14159 * 64ft^2 * 19ft
V_total ≈ 3.14159 * 1216ft^3
V_total ≈ 3817.876544ft^3
Therefore, the volume of the entire figure is approximately 3817.876544 cubic feet.