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galactus · Feb 29, 2008, 12:15 PM

Here's another challenge problem if anyone would like a go.

Please excuse my hackneyed paint drawing. I hope it's OK.

"A wedge is cut from a right circular cylinder of radius r by two planes, one perpendicular to the axis of the cylinder and the other making an angle @ with the first. Find the volume of the wedge by slicing perpendicular to the y-axis. Try it perp. to the x-axis."

ebaines · Feb 29, 2008, 03:46 PM

I get: $V= \frac 2 3 R^3 tan(\theta)$ .

Slicing perpendicular to y-axis gives:

$<br /> V = \int_0 ^R (R^2-x^2)tan(\theta) dx.<br />$

Slicing perpendicular to x-axis gives:

$<br /> V = 2 \int _0 ^R x tan(\theta) \sqrt{R^2-x^2} dx<br />$

galactus · Mar 1, 2008, 05:26 AM

That was too easy. I knew you'd get it, ebaines.:cool: I will have to think of something a little more challenging. Something along the lines of number theory? :)

ebaines · Mar 1, 2008, 07:18 AM

Galactus: I'll post one for you - the classic "bug problem."