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\textbf{Math 225: Calculus III}
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\textbf{Quiz 8}\quad \textsl{November 7, 2002}
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1. Let $E$ be the solid region in the first octant bounded by the
coordinate planes and the planes $2x+y=2$ and $2y+z = 2$. Express
$\iiint_E 3x\,dV $ as an iterated integral. (Do not evaluate the
integral.)

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2. Let $E$ be the solid region inside the sphere $x^2 + y^2 + z^2 = 2z$
(with center $(0,0,1)$ and radius $1$) and above the cone $z = \sqrt{x^2 +
y^2}$. Express $\iiint_E \sqrt{x^2+y^2+z^2}\,dV$ as an iterated integral in
spherical coordinates. (Do not evaluate the integral.)

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