Answer to Question #132924 in Geometry for x

Question #132924

A right-circular cone is inscribed in a sphere having a fixed radius of 10 in.
Express the volume of the cone as a function of its radius.

Expert's answer

By Pythagorean theorem we have 10²=R²+(H-10)²(see the picture).

Therefore, H = 10+(100-R²)^1/2; and V = "\\pi" (10+(100-R²)^1/2)R²/3.

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