Thread: Wedges and elilptical cylinder cross sections :(

1. Wedges and elilptical cylinder cross sections :(

if someone could help me start or point me in the direction of how to start this question that would be awesome

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A wedge is cut out of an elliptical cylinder whose cross-sections are given by the
ellipse

x^2/4+ y^2/9 = 1

One plane is perpendicular to the axis of the cylinder. The other one intersects the
fi rst at an angle of 60 along the shorter diameter of the ellipse (i.e. the x-axis if
you draw the ellipse in the usual xy-plane). Find the volume of the wedge

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2. Re: Wedges and elilptical cylinder cross sections :(

Originally Posted by Havok
how to start this question
A picture, preferably in your head, or someone may do it for you in Matlab, but maybe this will help you imagine it:

Between the x axis and this semi-ellipse is the base of your wedge. The wedge has a curved wall extending vertically i.e. in the z direction. It also has a flat sloped roof, which has a straight edge that meets all of the straight edge of the base, and which rises from the base at 60 degrees to it, and is semi-elliptical itself, because it disappears where it reaches the vertical elliptical wall.

So you can construct a double or triple integral that totals up a journey going from -2 to 2 or double 0 to 2 in the x direction, stopping at every point to take a detour from 0 to ... in the y direction, and stopping at every point again to take a detour from 0 to ... in the z direction.

Have a go with that?