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Depends on the direction of the slice.
1) Parallel to the base creates a circle.
2) But, parallel to the line from the vertex to the center creates a hyperbola.
3) Imagine a line along the side of the cone from the circumference of the base circle thru the vertex, now cut parallel to that line and create a parabola,
4) Last cut at any angle not parallel to any of those and you create an ellipse.
These are called the 4 conic sections.
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What is A thin flat piece cut from something?
maybe I think it's "slice"
How can you prove that the volume of a right circular cone is one third pie times radius square times height?
This is a nice bit of calculus. You sum up an infinite number of infinitely thin slices of the cone as follows: Radius of each slice = r*(h-x)/h Surface area of each slice = Pi*r2(h-x)2/h2 Integral of Pi*r2(h-x)2/h2 dx evaluated from 0 to h = Pi*r2*h/3
How surface area of a cone can be used in real life?
Practical applications include when you need to calculate how much material you need to make such a cone; how much paint you need to cover it; or when you want to find out the mass of the cone (the first and third examples assume it isn't a solid cone, but only has a thin layer).
How do you find volume of an irregular solid figure?
By integration - you divide the figure into many thin slices, and calculate the volume of each slice individually. The volume of each slice, again, can be calculated by integration: divide it into thin rectangles, and calculate the area of each rectangle. If you have a irregular solid figure just immerse it in water and measure the displacement. a la Archimedes
How was the formula for the volume of a pyramid developed?
I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)I am not sure how it was originally obtained. In some math book I saw how a specific triangular prism could be divided into three congruent pyramids.The formulat for the volume of a pyramid, or of a cone for that matter, can be obtained quite easily with calculus. The basic idea is to divide the pyramid into thin slices, and calculate the area of each (assuming that each slice is a rectangular block). You might do an approximation in Excel. The thinner the individual slices, the more accurate the result. (Calculus uses more advanced methods, to get the result quicker.)
