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A cylinder and a cone have the same height, but the base radius of the cylinder is only half that of the cone. If the volume of the cylinder is 1, then what is the volume of the cone

 Jun 12, 2021
 #1
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Assume the base area of the cylinder is $\pi r^2$. Thus, the base area of the cone is $\pi (2r)^2 = \pi 4r^2$.

 

It follows that the volume of the cone is $4$ times the area of the cylinder. 

 

However, the area of the volume of a cone is $\pi r^2 \frac{h}{3}$, notice the $\frac{1}{3}$. Can you solve the problem from here? 

 Jun 12, 2021
 #3
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yes! thank you, I really appreciate it!

 Jun 14, 2021

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