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You are not logged in. #2 20060127 10:16:36
Re: volume of cone provingThis works just like calculus, except you don't actually use an integral. times the sum of the first r perfect squares , by the formula for the sum of the first r perfect squares. The volume of a cylinder with the same base and height is The ratio of the area of the cone to the cylinder is therefore Note that if we had used a height other than r, the height would've canceled out anyway once we divided by the volume of the cylinder. Obviously, the more disks we have (the bigger r is), the more accurate the ratio will be. As r gets very very big, get's very very small, and get's very very small. At this point, note that since r is getting very very big, the assumption that it is an integer get's less and less important, because we are taking an infinte number of "samples". So effectively, the ratio is , and the volume of the cone is the volume of the cylinder. Volume of a cylinder is Area of base x Height, so the volume of a cone is 1/3 x Area of Base x Height Again, these kinds of approximations work just like calculus and are the foundation of calculus, but you should be able to understand it without calculus. PS  what is the latex tag on this forum? I'm sick of writing without latex... PPS  Thanks John Last edited by God (20060129 03:14:08) #3 20060127 14:44:52
Re: volume of cone provingT h e L a T e X t a g i s [ m a t h ]Equation here.[ / m a t h ]. igloo myrtilles fourmis 