Final answer:
To keep the base diameter and volume of both the cylinder and cone the same, the height of the cylinder is three times the height of the cone.
Step-by-step explanation:
To keep the base diameter and volume of both the cylinder and cone the same, we need to use the formulas for the volume of a cylinder and a cone. The volume of a cylinder is given by V = πr^2h, where r is the radius of the base and h is the height. The volume of a cone is given by V = (1/3)πr^2h.
Since the base diameters are the same, we can say that the radii are the same. Let's assume the height of the cylinder is h, and the height of the cone is x.
Using the formula for the volume of a cylinder, we have V = πr^2h = π(r^2)(h). To keep the volume the same, we need to set it equal to the volume of the cone, which is given by V = (1/3)πr^2x. Setting these two equal, we get π(r^2)(h) = (1/3)π(r^2)x.
Cancelling out π and r^2, we get h = (1/3)x. Therefore, the height of the cylinder is three times the height of the cone. So, the statement that is true is: The height of the cylinder is three times the height of the cone.
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