Find the volume of "A tetrahedron with three mutually perpendicular faces and three mutually perpendicular edges with lengths 3 cm, 4 cm, and 5cm."(adsbygoogle = window.adsbygoogle || []).push({});

This is how I visualized it:

http://img282.imageshack.us/img282/9466/calculus31re.th.jpg [Broken]

The area of a triangle along the x-axis is:

A(x) = .5 * x * (3/5x), 3/5x is from similar triangles.

A(x) = 3/10 * x^{2}

[tex]V = \int^{5}_{0} A(x) dx = \frac{3}{10} \int^{5}_{0} x^2 dx

= \frac{1}{10} [x^3]^{5}_{0}

= 12.5 cm^3[/tex]

But the answer is 10 cm^{3}. Why doesn't my method work?

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# Volume of a tetrahedron

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