# volume of a sold

by vigintitres
Tags: sold, volume
 P: 26 1. The problem statement, all variables and given/known data The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Cross-sections perpindicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the described solid. 2. Relevant equations V = {int} 1/2 b*h dy 3. The attempt at a solution I found that I would have to use the symmetry to solve this. The only things I have are x^2 + y^2 = 1/2 and y = sqrt(.5 - x^2) Now i know I have to integrate an isosceles triangles area which is 1/2 b*h but I'm not sure what the base or the height will be.
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P: 26,127
Hi vigintitres!
 Quote by vigintitres The base of S is an elliptical region with boundary curve 9x^2 + 4y^2 = 36. Cross-sections perpindicular to the x-axis are isosceles right triangles with hypotenuse in the base. Find the volume of the described solid. … I found that I would have to use the symmetry to solve this. The only things I have are x^2 + y^2 = 1/2 and y = sqrt(.5 - x^2)
Where do you get x^2 + y^2 = 1/2 from?

9x^2 + 4y^2 = 36.
 Now i know I have to integrate an isosceles triangles area which is 1/2 b*h but I'm not sure what the base or the height will be.
The base is 2y.

The height you can work out because it's a right-angled isoceles triangle.
 P: 15 Find volume via method of cross-sections.

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