circle problem

[smeag]

A pipe has an outside diameter of 1.25 inches and an inside diameter of .75 inches. if BOB hacksaws the pipe in two what fraction of the pipe cross sectional area is sawn when the blade breaks through to the inside?
Please explain soon and show your steps. Thanks!

[FabensMath]

First we need to find the radii:
1.25/2 = .625 and 0.75/2 = .375
using these two lengths, you can find the length of the chord:
sqrt{.625^2-.375^2) = 0.5
Length of chord: 0.5 * 2 = 1
So the angle half the angle of the segment is:
sin^-1(.5/.625) = 0.927295
Angle of segment: 0.927295*2 = 1.85459
Area of sector: r^/2(theta - sin(theta)) = .625^2/2(1.85-sin(1.85)) = .1747

Area of full pipe = pi(.625)^2 - pi(.375)^2 = .7854

Percentage: 100(.1747/.7854) = 22.2

I'm too lazy to put nice print right now, sorry. There's probably a shortcut to this one, i just haven't figured it out, this one is the long way.