Math Basic Geometry. Unit: Volume and surface area. Volume of a Cone. How does he solve for r^2

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Hi,

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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 :)