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PhysicsinCalifornia

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**HW problem--NEED HELP!**

This is an optimization problem with differential calc. I really need help with this

Here's the prob:

A right circular cone is being inscribed in a sphere of radius 3cm.

Find

a) the dimensions (base radius, and height) of the right circular cone with the largest volume

b) the cone's volume

Here's what I got::

Volume for sphere is

[tex]V_s = \frac{4}{3}\pi r^3[/tex]

and the volume for the cone is

[tex]V_c = \frac{1}{3}\pi r^2 h[/tex]

(obviously)

Now i got that [tex]h = 3+x[/tex]

*Note that I cannot draw a pic, so it's hard to describe

Also, [tex]x = \sqrt{9 - r^2}[/tex] using pythagorean's theorem

so the height would equal the radius of the sphere, 3 cm, plus x

Therefore

[tex] V(r) = \frac{1}{3} \pi r^2 (3 + \sqrt{9- r^2}) = \pi r^2 + \frac{\pi r^2 \sqrt{9 - r^2}}{3}[/tex]

leaving everything in terms of r because we want the largest volume

How do I work it from here?

Thanks for your help in advance

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