π is simply a ratio between the diameter, d (or twice the radius, r) of a circle and it's circumference. In other words, a circle that has a diameter of 1 or a radius of 1/2 will have a circumference of π. π is conveniently also the ratio of r squared (r times r) to the area of the circle, meaning that a circle with radius 1 will have an area of π. Let's take a look at some of your questions.
1) Here we've been given that the radius 6. Now we simply plug that into our equation for circumference and we find a circumference of 12π or about 37.7.
2) Now we have the circumference of the circle and want the radius so we rearrange our circumference equation to solve for r. We do this by dividing both sides by 2π to get: r = C/2π. Now we just plug in our circumference of 24π to get 24π/2π or 12.
3) We can solve this equation in three steps. First we use the equation from problem 2 to solve for the radius. Doing that will give us 16 as r. Now we plug 16 into our equation A = π(rsquared) to give us an area of 256π.
As you can see, all these questions can be solved by moving from what you are given (either the radius, the area, or the circumference) to what you need to solve. See if you can solve the next three problems on your own using what I have explained. For number 6, you need to solve for the original radius, double it, and then solve for the new area. Hope that helps!
1/9/2013

Daniel K.
Comments
Hey Courtney... Apparently the Answer section below isn't working...
p is just a definition: it's the ratio between a circle's diameter and its circumference. In other words, any circle circumference is approximately 3.14 (p) times longer (around) than its diameter length. Some old Greek dude discovered it a few thousand years ago... Let's do the first 3 problems together  by then I think you'll have confidence you can do the remaining 3!
1. If C = 2pr, then we substitute C = 2*3.14*6, = 37.68
2. If C = 2pr, then let's rearrange that so we can find r: divide both sides (to keep it equal) by 2p to get r by itself: C/2p = 2pr/2p, so r = C/2p. Now substitute: r = 24p/2p = 12
3. If C = 2pr, then r = C/2p (see #2 above), then r = d/2.
If A = pr^{2}, then A = p (C/2p)^{2}. Substitute: A = p (32p/2p)^{2}, or A = p (16)^{2}
A = 3.14 * 256 = 803.84
Now can you complete #3  #6? I bet you can... :)
I tried adding answers via Answers below, and also via Comments  no go!