Volume of Cones, Cylinders, and Spheres Quick Check
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Question
Use the image to answer the question.
A cone is placed inside a cylinder. The apex of the cone touching the center of the top circle of the cylinder is highlighted with a dot. The cone with its base is drawn in dashed lines. The base of the cone is common with the base of the cylinder.
A sculptor created a design by carving a cone out of a cylinder. The cone and cylinder share the same radius and height. If the volume of the cylinder before removing the cone is 54 in.3 , what is the volume of the amount remaining?(1 point)
The volume of the cone can be calculated using the formula V = (1/3)πr^2h, where r is the radius and h is the height. Since the cone and cylinder have the same radius and height, we can calculate the volume of the cone to be V = (1/3)π(3^2)(3) = 9π in^3.
Therefore, the volume of the remaining portion after removing the cone would be the volume of the cylinder minus the volume of the cone, which is 54 - 9π ≈ 25.13 in^3.