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Re: volume of a coneUsing Calculus, by integration, u need to arrive the volume of the cone #3 20070628 18:02:59
Re: volume of a coneok, this is how i'd do it: The Beginning Of All Things To End. The End Of All Things To Come. #5 20111016 02:46:39
Re: volume of a coneHi abegale; In mathematics, you don't understand things. You just get used to them. I have the result, but I do not yet know how to get it. All physicists, and a good many quite respectable mathematicians are contemptuous about proof. #6 20111016 09:17:55
Re: volume of a conehi so So think of a section of the pyramid made by an area s with a thickness of delta h. Use integration to add up all such volumes thus: So for any right* pyramid the volume is one third the height times the base area. *Right here means that the axis is at right angles to the base. It is relatively easy to adapt this proof for non right pyramids. Bob Last edited by bob bundy (20111016 09:18:22) You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #7 20111016 16:28:51
Re: volume of a cone
The volume of a right circular cone with radius r and height h, equals the area of the right triangle (let the base = r and the height = h), which is being revolved along the line containing the line segment h, multiplied by the circumference using the r/3 part of the centroid* as the radius of revolution. The centroid of a triangle is where all of its medians intersect. The centroid is the geometric center of the triangle.** Then the formula for the volume is the area of the triangle, multiplied by the circumference at the geometric center (centroid), and using r/3 as the radius of revolution. This is:   . .   . .   . .   . .   . .   . .   . .   * Suppose a right triangle is situated on the xyplane with the radius extending from (0, 0) to (r, 0) and the height extending from (0, 0) to (0, h). The xcoordinate of this centroid is r/3. (This can be worked out using coordinate geometry.) ** Source: http://en.wikipedia.org/wiki/Centroid Signature line: I wish a had a more interesting signature line. #8 20130520 03:31:21
Re: volume of a coneanyone explain to me where does the 1/3 of the formula of the volume of the cone and pyramid come from?need the answer ryt away. like what if without the idea first of having 1/3bh for their volume..how will we know it. or lets just say how to prove volume of the cone v=1/3bh .please in an understnding and clear way and as much as possible not just calculus..simple way ..thankss so much #9 20130520 05:09:11
Re: volume of a conehi moebhy Now if you had a cone with the same base radius and height, the volume would be less, wouldn't it. seems reasonable, doesn't I? I can take you step by step through the calculus if you wish. That way you'll learn some calculus too. Bob You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei #10 20130615 16:28:39
Re: volume of a coneWhy do I get the wrong answer when using the shell method? #11 20130615 18:01:26
Re: volume of a conehi anon,
If you rotate an isosceles triangle by 2pi you are generating the volume twice over as each halftriangle will make the whole solid. You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei 