Inscribed ConeDate: 3/11/96 at 18:47:33 From: Edward Tang Subject: Calc problem Hi - My Calculus teacher and I are having problems with this question: "Find the volume of the largest right circular cone that can be inscribed in a sphere of radius 'r'" It seems hard to relate 'r' with anything on the cone...... If that connection can be made, then the derivative can be found and the problem solved...... Thanks! - Ed Date: 6/21/96 at 11:48:14 From: Doctor Jerry Subject: Re: Calc problem Start by drawing a triangle inscribed in a circle of radius r. Draw it as a somewhat slender isoceles triangle, with the base between the equal sides placed on the bottom. Locate the center of the circle. Draw a line from the center to the lower left vertex and a line from the center to the base and perpendicular to it. You see a small right triangle. Let its lower base be called R. This is the base radius of the inscribed cone. The height of the inscribed cone is r plus the vertical side of the small right triangle. This side is sqrt(r^2-R^2). So, the volume of the cone, in terms of r and R, is V=(pi/3) R^2 (r+sqrt(r^2-R^2)). This function can be maximized without much trouble. I get R=2*sqrt(2) r/3. -Doctor Jerry, The Math Forum |
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