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Question

Consider the plane ax+by+cz=d, where a, b, c, and d are all positive. Use previous problem to show that the volume of the tetrahedron cut from the first octant by this plane is $d D /\left(3 \sqrt{a^2+b^2+c^2}\right)$, where D is the area of that part of the plane in the first octant.

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 9We can proved using the Gauss's Divergence Theorem that the volume of the solid enclosed by the surface $S$ is given by:

$V(S)=\dfrac{1}{3}\iint_{S}{\bf F}\cdot{\bf n}dS$

Where ${\bf F}=(x,y,z)$.

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