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Calc Help

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.JPolster
Posts: 782 - Karma: 17
A right circular cone is to be inscribed in a sphere of radius 5 cm. Find the maximum volume of the cone.

I have no idea how to do this.
Nov 28 2011 7:35PM
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*TURBONERD*
Posts: 15094 - Karma: 9,275
You serious? Radius and height of the cone is also 5 cm. So, it's (1/3)(pi)(5^2)(5), following the formula for cone volume, which is 1/3pi(radius)^2(height). Do the rest yourself.
Nov 28 2011 7:38PM
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.JPolster
Posts: 782 - Karma: 17
But to obtain the maximum area of the the cone, you wouldn't have it set up with a radius of 5. it would look like this i think

Click for larger image
Nov 28 2011 7:42PM
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p-fo
Posts: 9372 - Karma: 6,156
Cummings got it. This isn't even calc...
Nov 28 2011 7:43PM
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.JPolster
Posts: 782 - Karma: 17
if you have it set up with the cones radius of 5 that is not maximizing the area of the of the cone. To find it wouldn't you take the derivative of volume of a cone formula, but replace the r and the h with h=5+5cos(x) and r=5sin(x).
Nov 28 2011 7:49PM
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p-fo
Posts: 9372 - Karma: 6,156
Wait nevermind. I thought it said equilateral or something. It's a related rates problem. You gotta relate the radius to the volume of the cone, plug it into the cone volume equation and find that maximum. I don't feel like explaining more because it's been a year and I have stats homework to finish.
Nov 28 2011 7:50PM
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