How would I find the volume of a pyramid

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SUMMARY

The volume of a pyramid with an equilateral triangle base can be calculated using the formula V = (1/3) * A * h, where A is the area of the base and h is the height. The area of an equilateral triangle can be determined using the formula A = (sqrt(3)/4) * a^2, where a is the length of a side. The discussion emphasizes that the volume calculation involves integrating the area of cross-sectional slices of the pyramid as height varies. The correct formula for the volume incorporates both the area of the base and the height of the pyramid.

PREREQUISITES
  • Understanding of geometric formulas, specifically for pyramids and triangles.
  • Familiarity with calculus concepts, particularly integration.
  • Knowledge of the properties of equilateral triangles.
  • Basic algebra skills for manipulating equations.
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  • Research the derivation of the area formula for equilateral triangles.
  • Learn about the application of integration in calculating volumes of solids of revolution.
  • Explore advanced geometric concepts related to pyramids and their properties.
  • Study examples of volume calculations for various pyramid shapes.
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Students studying geometry, educators teaching mathematics, and anyone interested in understanding the principles of volume calculation for pyramids.

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How would I find the volume of a pyramid with an equilateral triangle as it's base? I know how to do a pyramid with a square base (the integral from 0 to it's height of 2*(equation solved for y of a side)^2 dy)). Would this be the same method?
 
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Didn't your text tell you that the area of a pyramid is 1/3 the product of the area of its base and its height?
 
You can make an equation for the area of a given slice of the pyradmid with respect to the height (since the height will determine the side length, which will of course influence the area since it is equilateral..I believe it's ((a)^(3/2))/4 but I forget.
 

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