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The volume of a cone is 27cm^3. What is the volume of a cylinder that shares the same radius and height as the cone?
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GPT 3.5
Given that the volume of the cone is 27cm^3 and the volume formula for a cone is V = (1/3)πr^2h, where r is the radius and h is the height.
We can rearrange this formula to solve for the height of the cone:
27 = (1/3)πr^2h
h = 27 / ((1/3)πr^2)
h = 81 / πr^2
Now, let's find the volume of the cylinder using the formula V = πr^2h:
V = πr^2 * (81 / πr^2)
V = 81cm^3
Therefore, the volume of the cylinder that shares the same radius and height as the cone is 81cm^3.
We can rearrange this formula to solve for the height of the cone:
27 = (1/3)πr^2h
h = 27 / ((1/3)πr^2)
h = 81 / πr^2
Now, let's find the volume of the cylinder using the formula V = πr^2h:
V = πr^2 * (81 / πr^2)
V = 81cm^3
Therefore, the volume of the cylinder that shares the same radius and height as the cone is 81cm^3.