volume of a sold


by vigintitres
Tags: sold, volume
vigintitres
vigintitres is offline
#1
Jul21-08, 05:15 PM
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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tiny-tim
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#2
Jul21-08, 06:06 PM
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tiny-tim's Avatar
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Hi vigintitres!
Quote Quote by vigintitres View Post
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.
ZharAngel
ZharAngel is offline
#3
Aug4-08, 03:52 AM
P: 15
Find volume via method of cross-sections.


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