A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup

link of picture of the cup is found in the attachement

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- November 9th 2006, 07:12 PMaaasssaaaOptimization problem, stuck
A conical drinking cup is made from a circular piece of paper of radius R by cutting out a sector and joining the edges CA and CB. Find the maximum capacity of such a cup

link of picture of the cup is found in the attachement - November 10th 2006, 04:52 AMSoroban
Hello, aaasssaaa!

Quote:

A conical drinking cup is made from a circular piece of paper of radius

by cutting out a sector and joining the edges and

Find the maximum capacity of such a cup.

Code:`..*.*.*..`

.*:::::::::::*.

A*:::::::::::::::*B

* *:::::::::::* *

R *:::::::* R

* *:::* *

* * *

* C *

* *

* *

* *

* * *

The side view of the cup looks like this:Code:`r`

*-----+-----*

\ : /

\ h: /

\ : / R

\ : /

\:/

*

where is the radius of the cone and is its height.

We see that: .**[1]**

The volume of a cone is: .**[2]**

Substitute [1] into [2]: .

Maximize

. . and we get: .

Substitute into [1]: .

Substitute into [2]: .

Therefore, the maximum volume is: .

- November 10th 2006, 04:09 PMaaasssaaa
Hey what program did you use to right your numbers, roots and pie in

- November 11th 2006, 01:15 AMCaptainBlack
The mathematical typesetting here is done using a LaTeX see this

(to see the code generating the equations quote the message and

you will see the typesetting codes embedded in the message).

RonL