Posted by Brad Paul on October 07, 2002 at 11:29:45:
In Reply to: cones posted by Kurt on October 07, 2002 at 10:16:59:
: 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
it.