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Math Forum / Mathematics / Recreational Math / June 2009Volume and radius of gyration
The area cut off from the parabola y^2 = 4ax by the latus rectum is rotated through four right angles about the directrix. Find the volume of the ring-shaped solid so generated and find the radius of gyration. Hi Ontadian, Unless I have made some errors the results are: Area = 8/3 * a^2 Volume = 128/15 * Pi * a^3 Inertia = 7424/315 * Pi * a^5 Radius of Gyration = sqrt(58/21) * a = 1.6619 a (approx) Regards, Peter Scales. Hi Peter, Correct result. Regards Bill. |
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