Re: Thanks; BUT how do I get an equation in order to maximize it???

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Posted by Subhotosh Khan on October 07, 2002 at 14:33:00:

In Reply to: Thanks; BUT how do I get an equation in order to maximize it??? posted by Kurt on October 07, 2002 at 14:15:06:

: : : A disk has a V cut to the centre and rolled and sealed into a cone.
: : : The cutout V is also rolled into a cone and sealed.
: : : What would the angle of the V be in order that the sum of the volumes of the two cones be a maximum?.

: : : Thank you in advance.
**************************************
1) Draw a picture of a circle - center at O

2) Draw an angle AOB - AB on the circumference of the circle. This is the piece you are cutting out.

3) Now for the smaller cone, The base is made out of circle whose circumference is AB (what is the length of AB if mAOB = T). From that you can get the area of the base(A_1). The height of the cone is R. So the volume of the small cone (V_1)=1/3*R*A_1

4) similarly find V_2 - the volume of Larger cone

5) V = V_1 + V_2 ... this will be function of 'T'(=mAOB)

6) differntiate and set it to zero to find maximum.

If need more help - show your work

: : Things you know and can calculate:

: : The distance from the top of the cone to the bottom along the edge of
: : the cone is the same for both cones and is equal to the radius of the
: : original disk.

: : You can find the circumference of both cones as a function of the
: : angle of the V.

: : From the circumference of the cone you can find the radius of the base
: : and then the height of the cone.

: : From the height and the radius you can find the volume of the cones.

: :
: : This is a simple problem with multiple steps. When doing a problem
: : with multiple steps try and break things down into simple pieces. Ask
: : yourself what can I calculate? Draw a good picture, start labeling
: : things in terms of what you know, even if you don't think you will need
: : it.

Follow Ups:

I tried and am lost, please show me how, thanks Kurt 20:44:52 10/07/02 (12)
- Show your work .. starting from step (3)..stating where do you get lost (n/t) Subhotosh Khan 08:30:17 10/08/02 (11)
  - starting from step (3).. Kurt 10:32:06 10/08/02 (10)
    - other questions Kurt 11:47:36 10/08/02 (9)
      - Answers to other questions Subhotosh Khan 12:09:22 10/08/02 (8)
        
        stepping in... Denis Borris 22:48:24 10/08/02 (7)
        
        Mr B... you lost me ...I'll do the full problem below Subhotosh Khan 10:22:54 10/09/02 (6)
        
        I got "unlost" .. Mr B you are partially correct Subhotosh Khan 11:21:17 10/09/02 (5)
        
        Mr B you are partially correct : I think I'm FULLY correct.... Denis Borris 12:53:27 10/09/02 (4)
        
        Hokay.... Denis Borris 16:26:44 10/09/02 (3)
        
        Please check your equation... Subhotosh Khan 16:53:07 10/09/02 (2)
        
        NO! Denis Borris 18:14:54 10/09/02 (1)
        
        Yes .... Subhotosh Khan 08:54:59 10/10/02 (0)

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: : : : A disk has a V cut to the centre and rolled and sealed into a cone. : : : : The cutout V is also rolled into a cone and sealed. : : : : What would the angle of the V be in order that the sum of the volumes of the two cones be a maximum?. : : : : Thank you in advance. : ************************************** : 1) Draw a picture of a circle - center at O : 2) Draw an angle AOB - AB on the circumference of the circle. This is the piece you are cutting out. : 3) Now for the smaller cone, The base is made out of circle whose circumference is AB (what is the length of AB if mAOB = T). From that you can get the area of the base(A_1). The height of the cone is R. So the volume of the small cone (V_1)=1/3*R*A_1 : 4) similarly find V_2 - the volume of Larger cone : 5) V = V_1 + V_2 ... this will be function of 'T'(=mAOB) : 6) differntiate and set it to zero to find maximum. : If need more help - show your work : : : : Things you know and can calculate: : : : The distance from the top of the cone to the bottom along the edge of : : : the cone is the same for both cones and is equal to the radius of the : : : original disk. : : : You can find the circumference of both cones as a function of the : : : angle of the V. : : : From the circumference of the cone you can find the radius of the base : : : and then the height of the cone. : : : From the height and the radius you can find the volume of the cones. : : : : : : This is a simple problem with multiple steps. When doing a problem : : : with multiple steps try and break things down into simple pieces. Ask : : : yourself what can I calculate? Draw a good picture, start labeling : : : things in terms of what you know, even if you don't think you will need : : : it.

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