SOLUTION: A cylinder is inscribed in a cone with height 10 and a base of radius 5, as shown below on the link. Find the approximate values of r and h for which the volume of the cylinder is

Question 912071: A cylinder is inscribed in a cone with height 10 and a base of radius 5, as shown below on the link. Find the approximate values of r and h for which the volume of the cylinder is a maximum. Then give the approximate maximum volume.
http://postimg.org/image/tewn41qu7/
Thank you!!
Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
There is a relationship between and .
When ,
When , .
So then using the point-slope form of a line,

So the volume of the cylinder is,

To maximize the volume, take the derivative of the volume and set it equal to zero (use the chain rule).

So then,

Then,

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