Question

Find the circumference of a circle that has the same area as a square that has perimeter 2 pi
A)2 root 2
B)pi root pi
C)pi/2
D)root 2/pi
E) 2

Answer 1

The area of the square is 2 pi * 2pi = 4pi^2
So,
\[4 \pi ^2 = \pi r^2\]r=\[r=2\sqrt{\pi}\]Circumference is:\[C=2 \pi r=2 \pi (2 \sqrt{\pi})=4\pi \sqrt{\pi}=4\pi^\frac{3}{2}\]

Answer 2

ah crap...

Answer 3

each side of the square is pi/2

Answer 4

so area is pi^2/4

Answer 5

so r= sqrt(pi)/2
C=pi*sqrt(pi)

Answer 6

my bad :P

Answer 7

ty

Answer 8

no prob

Answer 9

Ok @eseidl, where's my mistake?

Each side of the square will be \[\frac{2\pi}{4}\]Therefore the area of the square will be: \[(\frac{2\pi}{4})^2\]Which is equal to the area of the circle:\[(\frac{2\pi}{4})^2=\pi r^2\]\[r = \frac{\sqrt{\pi}}{2}\]

Answer 10

I got r= sqrt(pi)/2 as well...no error for either of us

Answer 11

Oh...duh. I'm getting tired :P

Answer 12

lol. the area of the square is (pi^2)/4 though

Answer 13

I don't see any mistake there...we just did it differently. It still works out to be pi^2/4 once I reduce.

Answer 14

yeah no prob. I would immediately reduce the the side of the square from 2 pi/4 to pi/2

Answer 15

no point in carrying the extra factor of 2 through the rest of the calculation

Answer 16

Yea...I just didn't think to reduce it at that point. Made slightly more work for myself