Calc Help

[.JPolster]

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.

 

[*TURBONERD*]

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.

 

[.JPolster]

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

 

[p-fo]

Cummings got it. This isn't even calc...

 

[.JPolster]

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).

 

[p-fo]

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.