+0  
 
0
36
1
avatar

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
avatar+12224 
+1

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.

laugh  !

 Sep 8, 2021

12 Online Users