https://support.khanacademy.org/hc/en-us/community/topics/115000487007-Study-Group

Hi,

Most people ask for clarification under the video, then if they need more help, they go over to the study group.

In this case, it would be best to post your question in the discussion area under this video: https://www.khanacademy.org/math/geometry/hs-geo-solids/hs-geo-solids-intro/v/volume-cone-example

By posting your question directly under the video, this gives us the most context for your question and will help ensure someone with the required knowledge to answer your question is able to see it.

I just looked at the problem and helped you through the basic algebra he doesn't go into detail about:

as you probably know, r^2 is the radius squared. So its a matter of finding the radius. 

The formula for the volume of a cone is 1/3(pi)*h*r^2, or in other words, the area of a cylinder(h * pi * r^2) divided by three.

The problem says that the area is equal to 131cm^3 and the height is 5 so substitute that in the equation

Then you will get 131cm^3(area) = 1/3(pi)*5(height)*r^2

Then you rearrange this

I will go over it step by step and in a bit more detail than he does

first multiply both sides by three(opposite of 1/3): 131*(3)=1/3*(3)*5*r^2*pi

If you notice, 1/3*3 = 1 and then that simplifies to 1*5*r^2*pi, but if you think about it, multiplying 1 results in the exact same number you multiplied 1 by. That means that 1*5*r^2*pi = 5*r^2* pi

Now we have the equation 131*3=5*r^2*pi

then we divide both sides by 5: (131*3)/5=5/5*r^2*pi

as I stated earlier 5/5 =1 

that means that the equation translates to : (131*3)/5=1*r^2=r^2*pi

that means : (131*3)/5=r^2*pi

(multiplying 1/pi is the same as dividing it)

Then we divide pi on both sides resulting in (131*3)/5 * 1/pi = r^2*pi*1/pi

pi * 1/pi =1 and (131*3)/5 *1/pi = (131*3)/(5*pi)

then the final equation is (131*3)/(5*pi)=r^2

that is how he got r squared(he did this part in his head because on a test you would probably do it in your head, but that's how he got r^2)

I hope this helps :)