r = R(1-x/2pi)
h = sqrt( R^2 - ( R (1-x/2pi)))
these are put into the formula for the volume of the cone. Now I need to derive that equation to know which x will give the max volume of the cone.
I can't figure out how to derive this. This is the formula for the volume of a cone. R is a constant and the side of the cone. Can be any real number.
If anyone could take a crack at deriving this id be very greatful!
V = \pi/3 * (R(1 - x/2\pi))^2 * \sqrt{(R^2 - (R(1 - x/2\pi))^2}
I have the answer now and it seems 1.84 radians was correct!
Question number two is next. Is it possible to set V = V1 + V2 and just derive that do you think?
I think I've got it. Could you please explain how you derived the above. I don't fully understand how to derive when there are square roots involved.
thanx!
The optimum angle is 1.84... radians then? Will try your method to see if i fully understand it. I'm writing a small paper on this so I might need to find the proof that max volume is given by that triangle. I can find that myself though probably. Thanx. Then i still have question 2 to figure...
Ok I've been working with this. I thought I would make the algebra easier by deciding the radius of the disc to be 1. Since it's constant it shouldn't matter which value i put here right.
That gave me the following:
r=(1-X/2\pi)
h=(1-(1-X/2\pi)
R = 1
V =...
But that still leaves too many unknowns?
I need both the radius of the cone. the height. and the angle (which is what I am looking for really).
I will continue in the morning, doing this at midnight is not a good idea =).
thanx for helping
thanks for the help mate, appreciate it. I am not native in english, but of course disc was the word to use :redface:
Im still having problems figuring this out.
the section cut away is \alpha*r
the remaining circumference of the disc, thus the base of the cone is
(a - \alpha*r)...
Hello, I have a problem I can't solve. Need assistance! :bugeye:
You cut out a piece of a circle (like you cut a piece of a cake), then make a cone by joining the edges of what remains of the circle. What angle must the "cakepiece" have to maximize the volume of the resulting cone?
I...