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# Cone

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a cylinder and a cone have the same height, but the base radius of the cylinder is only 1/3 of that cone. If the volume of the cylinder is 7, then what is the volume of the cone?

Sep 8, 2021

#1
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If the volume of the cylinder is 7, then what is the volume of the cone?

Hello Guest!

$$r_{cyl}=\dfrac{r_{con}}{3}\\ V_{cyl}=pi (\dfrac{r_{con}}{3})^2h=7\\ \dfrac{(r_{con})^2}{9}=\dfrac{7}{\pi h}\\ \color{blue}(r_{con})^2=\dfrac{63}{\pi h}$$

$$V_{con}=\dfrac{1}{3}\pi h\cdot (r_{con})^2=\dfrac{1}{3}\cdot \pi h\cdot \dfrac{63}{\pi h}=\dfrac{63}{3}\\ \color{blue}V_{con}=21$$

The volume of the cone is 21.

!

Sep 8, 2021