Surface Area Problems
Ratio Test

Evaluate each one of the following:

    \begin{eqnarray*} &&\int_{0}^{1}\int_{0}^{1-x}\int_{0}^{2-2x}dydzdx \\ &&\int_{0}^{1}\int_{0}^{z}\int_{0}^{y}dxdydz \\ &&\int_{0}^{1}\int_{0}^{1-x^{2}}\int_{0}^{1-x}dydzdx \\ &&\int_{0}^{\pi /2}\int_{x}^{\pi /2}\int_{0}^{xy}\cos \frac{z}{x}dzdydx \end{eqnarray*}

Use triple integral to find the volume of the tetrahedron bounded by 2x+3y+4z=1 in the first octant.

Use triple integral to find the volume of the solid bounded by z=x^{2}+y^{2} and z=18-x^{2}-y^{2}.

Use triple integral to find the volume of the solid bounded by z=4-y^{2},z=9-x and xy-plane.

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