radius

volume = pi r^2 x h

sqrt(volume/(pi x h)) = r

If you think about this, we can easily figure out the radius. It might take some thinking, however. The area of a cylinder is [Area of Base]*Height, or, in this case, Volume= π*r²h. For this case, we need to find the radius. Usually people use this formula to find the volume, but since we already have the volume and height,  we can plug the values we have into the cylinder volume formula and use algebra to find the radius! 

 

In this case, I want to show you an EXAMPLE. Let's say that the height is 10 meters, and the volume is ≈ 125.66. We can plug these into the formula(let's also say that pi ≈ 3.14). Our formula, with the values plugged in, would equal 125.66= 3.14* r^{2 *} 1o.

Taking this, we can simply multiply 3.14r² by 10, giving us the new equation 125.66= 31.4r² 

 

We now simply divide each side by 31.4, giving us the equation(rounded to the nearest tenth), 4 = r². [The actual calculation was 4.00191082803, which cannot be rounded to the nearest tenth. Therefore, it became a whole number]

 

Now we can take the square root of each side to find the radius. 4= r^2 = {r=-2, r=2}. We know that, since we are talking about lengths, we can't have a negative length. Therefore, the radius(r)≈ 2, which was the number I chose when I planned the problem.

 

Hopefully this helps you realize that you can use the volume formula and work it algebraiclly to help you find a missing length in a cylinder.