Show your work .. starting from step (3)..stating where do you get lost (n/t)

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Posted by Subhotosh Khan on October 08, 2002 at 08:30:17:

In Reply to: I tried and am lost, please show me how, thanks posted by Kurt on October 07, 2002 at 20:44:52:

: : : : : 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:

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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