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An equilateral triangle is rotated about one its altitudes, sweeping out a cone in space. If the side length of the equilateral triangle is $12 \sqrt{3},$ then find the volume of the cone.

 

Please help, I really don't know what to do!

 Feb 27, 2020
 #1
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The  side  length is  12√3   ...... 1/2   of  this is the  radius of the  cone  6√3

 

The  height  of the  cone =  6√3 * √3 =   6 * 3  =  18

 

So....the volume  of this rotated  equilateral triangle will be a cone with a radius  of 6√3  and a height of  18

 

So  .....the  volume  is

 

(1/3) pi * radius^2  * height  =

 

(1/3) pi * (6√3)^2 ( 18) = 

 

6 * 108 pi  =

 

648 pi  units^3

 

 

 

cool cool cool

 Feb 27, 2020
 #2
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Thanks for trying, CPhill, but that's wrong... anyone else?

Guest Feb 28, 2020

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