Pi R Square, but this is a circle

March 16, 2012 11:52 AM

Please help me with some basic math: The circumference of a circle is 8 inches. Extend that circle by 8 inches from circumference (i.e. adding 16 inches to the diameter). Now what is the circumference of the larger circle?

I am not in class, this is not a homework assignment. I *know* I should be able to do this basic math, but it's been too many years and major brain damage since I was in school.

posted by _paegan_ to Education (21 answers total)

Circumference = diameter x pi

I don't understand quite how you're enlarging the circle, though. What does 'from circumference' mean?
posted by hoyland at 11:55 AM on March 16, 2012

Unless I'm misunderstanding something, you've got a circle with a 24-inch diameter, so the circumference would be 24pi.
posted by griphus at 11:56 AM on March 16, 2012

C1 = 2*pi*r1
r1 = 2*pi/C1

r2 = r1 + 8 = 2*pi/C1 + 8
C2 = 2*pi*r2 = 2*pi*(2*pi/C1 + 8) = 4*pi^2/C1 + 16*pi
C1 = 8
C2 = pi^2/2 + 16*pi = 55.2 inches, approximately
posted by bfranklin at 11:57 AM on March 16, 2012 [1 favorite]

If the circumference is 8 inches, then its diameter is 2.54 inches. If you add 16 inches to that diameter, you'd have a circle with a diameter of 18.54 inches. Multiply that by pi and you'd have a circle with a circumference of 58.27 inches.

But I agree with hoyland- I'm not sure what you mean by "Extend that circle by 8 inches from circumference."
posted by thewumpusisdead at 12:00 PM on March 16, 2012

Wait, I did misunderstand something. If the circumference of the original circle is 8, the radius would be 4/pi.

So to find the circumference of a circle of that radius with an additional 8 inches to its radius, you'd be doing:

2*pi*((4/pi)+8))

...which is...

8+16pi

So the circumference of the new circle would be 8+16pi, or about 58.24 inches.
posted by griphus at 12:03 PM on March 16, 2012

First, find the diameter of the first circle. You know the circumference is 8, so...

d = 8 ÷ π
d = 2.55

OK. Add 16 for the diameter of the new circle...

2.55 + 16 = 18.55

Now you just have to find the circumference...

c = π × 18.55
c = 58.28

(The slight variations we're getting has to do with how many decimal places we go with π and how we round the results. bfranklin has me scratching my head, though...)
posted by Sys Rq at 12:20 PM on March 16, 2012

Let's get some definitions in here:

The radius (R) is the distance from the center to the edge.

The diameter (D) is the distance from one edge to the opposite edge. It is twice the radius.

D = 2*R

The circumference (C) is the distance around the outside.

C = pi * D = 2 * pi * R
posted by Chocolate Pickle at 12:21 PM on March 16, 2012

and while we're correcting things pi *r^2 is the area.
posted by empath at 12:24 PM on March 16, 2012

Response by poster: If it helps why I'm so confused and confusing... I'm sewing wrist cuffs that need to create a full circle when spread out. The part (gathered) at the wrist is to be 8 inches around. The cuff is to be 8 inches from wrist to finger. Since I will be gathering a long length, I need to know how much to cut. From your answers, it looks to be about 58 inches. But I may have asked the question worse than commentors have imagined - that seems like A LOT of fabric.

And, seriously, I really do have brain damage and it hinders my communication skills. I am not a troll. empath is onto why I had so much trouble with the math in the first place... remembered wrong formula.
posted by _paegan_ at 12:30 PM on March 16, 2012

If it really has to create a full circle when spread out, then 58 inches is correct. But it will look like a wizard sleeve facing away from the hand.
posted by scose at 12:42 PM on March 16, 2012

Maybe you can draw a diagram of what's going on? That'll help us figure out what exactly you want to ask.
posted by griphus at 12:43 PM on March 16, 2012

C = πD. So for every inch of diameter you add, you add π inches of circumference. Regardless of the size of the initial cirlce. So if you're increasing the radius by 8 inches, you are increasing the circumference by 8 * 2 * π = 50.2654... inches
posted by aubilenon at 12:46 PM on March 16, 2012

I think you actually asked the question correctly, it's just kind of unexpected.

So: you're going to be creating a circular piece of fabric with a circular cutout in the middle. The inner cutout has a circumference of 8". And the outer circle will extend 8" beyond that. Right.

So the radius of the inner cutout is (8/pi)/2 = 1.25" (a tiny bit more actually). Add 8" to that. That's the radius of your big circle, 9.25" So it has a diameter of 18.5", and a circumference of 58".
posted by adamrice at 12:47 PM on March 16, 2012

I think the OP means the type of cuff in drawing B here, but much fuller because it's longer. So the inner circle of 8" circumference is the measurement around the wrist.
posted by essexjan at 12:49 PM on March 16, 2012

So, for a circle with a circumference of 8", the radius is 1.27324 inches, say 1.25.

Add 8" to that, 9.25 for your radius. This gives a total circumference of 58"

I'm not a mathematician, but there's an online calculator here.

If you're adding the circular cuff to the end of the sleeve, gathered in at the wrist, you'll need to cut a circle that's 18.5" across, and cut the 8" circle out of the middle
posted by essexjan at 1:03 PM on March 16, 2012

Yeah, retracting my answer. I went wrong in step 2 -- r1 = C1/(2*pi). Ah well, that will happen when I try to solve in a text box rather than on paper.
posted by bfranklin at 1:04 PM on March 16, 2012

Actually, if you cut the 8" circle, you won't need to gather it if it's the same size as the wrist opening. This sounds awesome.
posted by essexjan at 1:05 PM on March 16, 2012

Arrrgh, no, not an 8" circle, a circle that has a diameter of 2.5" (for a circumference of 8")
posted by essexjan at 1:06 PM on March 16, 2012

_paegan_ if you're asking how much MATERIAL you'll need to cut out your cuff pattern, the answer is 1.41 ft x 1.41 ft. (or 1.5 ft x 1.5 ft - just to be safe) i.e. about 2 sq ft.
posted by sedunova at 1:08 PM on March 16, 2012

Response by poster: Well, I wasn't planning to cut a large circle with a smaller circle cut out for the wrist opening but that may be the better option. I was planning to use a long length of 8" x n fabric, stitched and gathered into a circle. n being the circumference of the larger circle that I asked about.

However, now my brain hurts so I'm just going to cut the larger circle with the smaller circle removed from the center.

The cuff is something like this.
posted by _paegan_ at 1:37 PM on March 16, 2012

Paegan now that I see your explanation, I definitely give you two thumbs up for abstract thinking. :) I hope the sewing works out.

I calculate a 58" circumference, incidentally (literally on the back of an envelope).
posted by Sutekh at 4:09 PM on March 16, 2012