# Proof #2

1. Apr 29, 2007

### ND3G

If a circle has an area of t square units and radius r, then a circle with area 2t square units has a radius 2r

a) State whether or not the statement is true, Justify your answer.

b) If it is not true, rewrite the statement so that it is true.

50 = (4)(4)(pi)
100 = (5.6)(5.6)(pi)

5.6/2 does not equal 4, therefore the statement is false.

If a circle has an area of t square units and radius r, then a circle with area 4t square units has a radius of 2r.

50 = (4)(4)(pi)
200 = (8)(8)(pi)

Does this look ok?
I know, I ask a lot of questions but I want to make sure I understand this stuff

2. Apr 29, 2007

### Dick

Aside from the fact that at some point you should have enough confidence to stop asking questions and start trusting yourself. It looks GREAT.

3. Apr 29, 2007

### Dick

Well, and 4*4*pi does not equal 50. I think you are more right in spirit than in literal fact.

Last edited: Apr 29, 2007
4. Apr 29, 2007

### christianjb

4pi^2 = 50 to two sig. fig.

That's good enough for government work.

5. Apr 29, 2007

### Dick

True. Just experimenting with the numbers is a great first step. But you did mean 4^2*pi, right?

6. Apr 29, 2007

### ND3G

Yeah, I rounded off the numbers so the example wouldn't be overly messy and since the proof is what the question is really asking for.

Thanks again guys

7. Apr 30, 2007

### Integral

Staff Emeritus
You really do not need to, and should not, use specific numbers in this type of problem.
you are given this to be true:
$$t = \pi r^2$$

now what is the area for a circle with radius 2r?

$$\pi (2r)^2 = 4 \pi r^2 = 4t \neq 2t$$

So the given statement is false.

8. Apr 30, 2007

### Hurkyl

Staff Emeritus
This is in a geometry class, right? I strongly suspect that whoever wrote the question did not intend for you to invoke the area formula of a circle. (Unless they're building up to the easy way to do this problem)

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