An easier (but still good) math problem to test your geometry skills.

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J

Jothaxe

Golden Member
Apr 5, 2001
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Here is the diagram for the problem.

The circles are concentric and the line segment begins tangent to the inner circle, ending where it intersects the outer circle. The segment has length 1 inch.

What is the area between the circles in square inches? - Show your work

 
S

stndn

Golden Member
Mar 10, 2001
1,886
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link

and the area between the circles?
it's "the area of the big circle minus the area of the small circle" square inches :p

naaa... i'm too lazy to be thinking at this point :)

-529-
 
J

Jothaxe

Golden Member
Apr 5, 2001
1,274
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<< NO, im not doing your homework. ;) >>



This is sarcasm, right?

*jothaxe shuffles to replace the batteries in his sarcasm-meter*
 
P

pulpp

Platinum Member
May 14, 2001
2,137
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why the hell are we supposed to solve math problems here? you are missing school or something ? :)
 
P

ProviaFan

Lifer
Mar 17, 2001
14,993
1
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/* it's &quot;the area of the big circle minus the area of the small circle&quot; square inches */

Well, it's not quite that simple. The solution will probably involve some trig, which since I haven't studied that yet, I don't have the slightest idea how to do :)
 
Q

Quaggoth

Senior member
Jun 23, 2000
800
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just something to do.

I have no idea jothaxe, but I think pi(r2) has something to do with it. actually that's for figuring the volume of a sphere isn't it? anyway.

Concentric just means they have the same center correct?
 
J

Jothaxe

Golden Member
Apr 5, 2001
1,274
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<< why the hell are we supposed to solve math problems here? you are missing school or something ? :) >>



Pathetic though it may sound, I am missing it. :( I get pretty bored during the summer, so I like to try to keep my reasoning skilled sharp. :)

And actually I started this thread at the request of Quaggoth.

-jothaxe
 
P

ProviaFan

Lifer
Mar 17, 2001
14,993
1
0
Well then wtf doesn't somebody just pull up that calculator buried deep in the start menu and figger the dang thing out? :D
 
J

Jothaxe

Golden Member
Apr 5, 2001
1,274
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0


<< Concentric just means they have the same center correct? >>



Correct



<< I think pi(r2) has something to do with it. actually that's for figuring the volume of a sphere isn't it? >>



Actually, spheres have volume (4/3)*pi*r^3.

The area of a circle is just pi*r^2 as you said.

And the problem uses only a small amount of geometry and algebra. Once you see the trick the algebra is very brief.
 
J

Jothaxe

Golden Member
Apr 5, 2001
1,274
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<< Is the answer just Pi?
If it's correct I'll post my working. >>



Yes, this is the correct answer. And very quickly too. :)
 
Triumph

Triumph

Lifer
Oct 9, 1999
15,031
14
81
without looking at the rest of your answers (honestly) the answer is Pi.

good little problem. i love math like this.
 
H

Haircut

Platinum Member
Apr 23, 2000
2,248
0
0
I've got a digicam pic of my working (my scanner is broken at the minute :( )
It's not too clear but I think you can make most of it out.
Circle problem
 
N

nd

Golden Member
Oct 9, 1999
1,690
0
0
Pretty easy, here's what I did to get ~3.14159265359 inches.

1) Let R = the radius of the larger outside circle, and r = the radius of the smaller circle on the inside.

2) Find an equation to relate R to r. Do this by drawing a triangle. Draw a line from the center point to the left end of the line segment (note that this line equals the value &quot;r&quot;), and see the triangle. You have a triangle with two sides of length r and 1, and a hypotenuse of length R. Pythagorean theorem shows that R = sqrt(r^2 + 1) obviously.

3) Area of space between circles = pi*R^2 - pi*r^2 = pi(R^2 - r^2). Substitute sqrt(r^2 + 1) for &quot;R&quot; in this formula and the r's cancel out, leaving you with pi.

A little too easy..
 
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