What is the equation of the area of the ellipse when a cylinder of radius x is cut by a plane inclined at an angle a.

Angle a is the angle between the plane and the axis of the cylinder. If a is 90 then what we get is a circle of radius x.

PS. Consider the cylinder to be very long so that the plane cuts the cylinder completely

Any hints please?


You can use some trigonometry to find the length of the major axis. A little thought should convince you that the length of the minor axis is $2x$. This is all the information you need to find the area.

  • 1
    $\begingroup$ (+1) Exactly. We get $A=\frac{\pi x^2}{\sin\alpha}$. $\endgroup$ – Jack D'Aurizio Dec 11 '14 at 0:57

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