Cylinder is in the sphere. Radius of sphere is r. What is the biggest volume of cylinder then ?

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- December 15th 2006, 02:36 PMtotalnewbieWhat is volume of cylinder ?
Cylinder is in the sphere. Radius of sphere is r. What is the biggest volume of cylinder then ?

- December 15th 2006, 03:52 PMSoroban
Hello, totalnewbie!

Quote:

Cylinder is inscribed in a sphere of radius .

What is the biggest volume of cylinder then?

Code:`* * *`

* - - - - - *

* | | *

* | | *

| |

* | | *

* | * | *

* | : \ | *

| h: \R |

* | : \ | *

* | : r \| *

* - - + - - *

* * *

The radius of the cylinder is .

The height of the cylinder is .

The volume of the cylinder is: .**[1]**

In the diagram, we see that: .**[2]**

Substitute**[2]**into**[1]**: .

Therefore, we must maximize: .

. . Go for it!

- December 15th 2006, 05:32 PMgalactus

So,

=

for .

, when .

Volume is largest when and - December 16th 2006, 04:46 PMtotalnewbie
And then area of Cylinder side is

Am I right ?