Finding the volume of a cone with a elliptic base

[Ahlahn]

Finding the volume of a cone with a elliptic base!

Homework Statement

The area of an ellipse is (pi)ab, where a and b are the lengths of the semimajor and semiminor axes. Compute the volume of a cone of height h = 20 whose base is an ellipse with semimajor and semiminor axes a = 4 and b = 6.

Homework Equations

The Attempt at a Solution

I tried to use the law of similar triangles to obtain the area of the elliptic at the cross section.

4/20 = a/20-y and 6/20 = b/20-y
b=6(20-y)/20 and a = 4(20-y)/20

Since the area of an elliptic is (pi)a*b, I tried to integrate by plugging in the above equations for a and b on the interval [0,20]. I failed.

HELP!

 

[Dick]

You've set up the problem exactly correctly. The volume is (1/3)*pi*a*b where a=4 and b=6. The integral also gives you (1/3)*pi*a*b where a=4 and b=6. How exactly did you 'fail'?