Consider the tetrahedron with vertices

(0,0,0)

(0,1,2)

(0,2,0)

(3,0,0)

Find its volume using integration. (No double or triple integrals though)

Printable View

- Feb 10th 2010, 12:34 PMzhupolongjoeTetrahedron volume
Consider the tetrahedron with vertices

(0,0,0)

(0,1,2)

(0,2,0)

(3,0,0)

Find its volume using integration. (No double or triple integrals though) - Feb 10th 2010, 12:38 PMicemanfan
Find a formula in terms of z for the area of a cross-section of the tetrahedron by a plane parallel to the xy-plane, and then integrate:

,

where is the area of the cross-section. - Feb 10th 2010, 01:35 PMzhupolongjoe
Thanks, but I'm not sure how to find A(z)

- Feb 10th 2010, 01:43 PMicemanfan
First, observe that the dimensions of the triangle decrease linearly as you move from z = 0 to z = 2. Therefore,

The length in x is equal to

The length in y is equal to

The area of the triangular cross-section is . - Feb 10th 2010, 03:15 PMzhupolongjoe
Okay, I see what you did. Sorry, but the only thing I still don't understand is how you got 3-1.5z. I understand the 2-z I think, but not this part.

EDIT::Nevermind, got it!