# Video: Solving a Given Formula for a Variable and Evaluating It at Given Values of Other Variables

The circumference of a circle as a function of its radius is given by πΆ(π) = 2ππ. Express the radius of a circle as a function of its circumference, denoting it by π(πΆ), and then find π(36π).

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### Video Transcript

The circumference of a circle as a function of its radius is given by πΆ of π equals two ππ. Express the radius of a circle as a function of its circumference denoting π of πΆ and then find π if the circumference is 36π.

Hereβs what we know. That finding the circumference in terms of π equals two ππ. This formula helps us find the circumference if weβre given the radius. We wanna transform this function into something that looks like this: π of πΆ. And that would help us find the radius if we were given the circumference. So where should we start? We wanna start by isolating this variable β getting the π by itself.

Right now, π is being multiplied by two π. I can use the multiplicative inverse of two π one over two π to multiply these values together equals one. In other words, they cancel each other out: two π times one over two π equals one. But the multiplication property of equality tells me that if I multiply by something on one side of the equation, I have to multiply by the same thing on the other side. So now we have to multiply the circumference by one over two π.

Now, we have the circumference divided by two π equals π. Because the circumference is no longer a function of the radius anymore, weβre going to just write πΆ to represent the circumference. And because the radius is now a function of the circumference, we can write π of πΆ. Just for clarity and because thatβs how we usually write a function, Iβll move that π of πΆ to the left and say the radius as a function of the circumference equals the circumference divided by two π; thatβs here.

Our next step will be to solve for the radius if weβre given a circumference of 36π. So weβve plugged in 36π , where our circumference πΆ variable was 36 divided by two equals 18 and π divided by π equals one. The radius of a circle with a circumference 36π equals 18. And here is our reordered formula that helped us find that.