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JA
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If the cylinder and the cone shown have the same volume, then the radius
and height of the cone could be which of these?
(2 points)
radius of the cone = 5; height of the cone = 12
radius of the cone = 15; height of the cone = 4
radius of the cone = 15; height of the cone = 12
radius of the cone = 5; height of the cone = 4
To find the volume of a cone, we use the formula V = (1/3)πr^2h, where r is the radius and h is the height.
Given that the volume of the cone is equal to the volume of the cylinder, and the volume of a cylinder is V = πr^2h, we can set up the equation:
(1/3)πr^2h = πr^2h
Solving for h, we get:
(1/3) = 1
r^2h = r^2h
This equation is true for any values of r and h, as long as they satisfy the requirement that the volume of the cone equals the volume of the cylinder. Therefore, all of the given combinations of radius and height are possible.