Friday

December 19, 2014

December 19, 2014

Posted by **DJ** on Sunday, October 16, 2011 at 5:41pm.

- Calculus -
**Steve**, Monday, October 17, 2011 at 11:42amDraw a diagram, with the top of the cone at the top of the sphere. If the cone extends past the diameter of the sphere of radius R, its base will have a radius r, and height h > R.

From the center of the sphere, draw a radius to the base of the cone. Then

r^2 + (h-R)^2 = R^2

r^2 + h^2 - 2rR = 0

Now, the cone has a volume of V = 1/3 πr^2 h

To avoid a bunch of square roots, let's square things:

V^2 = 1/9 π^2 r^4 h^2

= π^2/9 r^4 (2Rr - r^2)^2

2VV' = 4π/9 r^3 (2Rr - r^2)^2 + 2π^2/9 r^4 (2Rr-r^2)(2R-2r)

Now, V' is a bunch of stuff all divided by V. V is not zero, so V' will be zero when the numerator is zero. Toss out all that π^2 stuff, and we are left with a bunch of algebra that ends up giving h = 4/3 R.

That will give you the value of r.

do a google for maximum volume cone inscribed in sphere to find more details.

**Answer this Question**

**Related Questions**

Calculus - A right circular cone is inscribed in a sphere of radius r. Find the...

Math - A sphere is inscribed in a right cone. The slant height of the cone = the...

Calculus - A cone is inscribed in a sphere of radius a, centred at the origin. ...

math - A right circular cone is inscribed inside a sphere. The right circular ...

maths - Two spheres of radius 6 cm and 4cm are inscribed in a right circular ...

Geometry 10th - A cone is inscribed in a sphere with a radius of 5 centimeters....

Calculus - Given a right circular cone, you put an upside-down cone inside it so...

math - Two right circular cone, one upside down in the other. The two bases are ...

Math - (a) A sphere of radius 4 in is inscribed in a cone with radius 6 in. How ...

calculus - A paper cone is to be formed by starting with a disk of radius 9cm, ...