Posted by Kurt on October 07, 2002 at 14:15:06:
In Reply to: Re: cones posted by Brad Paul on October 07, 2002 at 11:29:45:
: : 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.
: 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
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