- #1
RolloJarvis
- 5
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Homework Statement
Find the volume of curved wedge that is cut from a cylinder of radius 3m by two planes. One plane perpendicular to the axis of the cylinder, the other plane crosses the first plane at a 45 degree angle at the centre of the cylinder.
(Hint: let the line of intersection of the two planes be the y-axis and then the cross section of the slice is a rectangle whose area you need to find as a function of x)
Homework Equations
V = [tex]\int^{b}_{a}A(x) dx[/tex]
The Attempt at a Solution
I need to find the area of the rectangle described above as a function of x so i can integrate it to find the volume.
The length of the vertical sides of the rectangle will given by the function y=x/2, and i presume the horizontal sides would be some function involving sin, seeing as is starts at 0, ends at 0, and has a maximum or 2r in the middle of the cylinder... but i can't figure it out. this is the bit I am stuck on.
Thanks for the help!