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# (Solved): Consider the function $$f$$ and region $$E$$. $f(x, y, z)=y, E=\left\{(x, y, z) \mid 1 \leq x ... Consider the function $$f$$ and region $$E$$. \[ f(x, y, z)=y, E=\left\{(x, y, z) \mid 1 \leq x^{2}+z^{2} \leq 9,0 \leq y \leq 1-x^{2}-z^{2}\right\}$ (a) Express the region $$E$$ in cylindrical coordinates. \begin{aligned} E &=\left\{(r, \theta, z) \mid 1 \leq r \leq 3,0 \leq \theta \leq \pi, 0 \leq z \leq 1-r^{2}\right\} \\ E &=\{(r, \theta, z) \mid 1 \leq r \leq 9,0 \leq \theta \leq 2 \pi, 0 \leq z \leq 1-\\ \left.r^{2}\right\} & \\ E &=\{(r, \theta, z) \mid 1 \leq r \leq 9,0 \leq \theta \leq \pi, 0 \leq z \leq 1-r\} \\ & E=\{(r, \theta, z) \mid 1 \leq r \leq 3,0 \leq \theta \leq 2 \pi, 0 \leq z \leq 1-\\ \left.r^{2}\right\} & \\ E &=\{(r, \theta, z) \mid 1 \leq r \leq 3,0 \leq \theta \leq 2 \pi, 0 \leq z \leq 1-r\} \end{aligned} Express the function $$f$$ in cylindrical coordinates. $f(r, \theta, z)=$ (b) Convert the integral $$\iiint_{E} f(x, y, z) d V$$ into cylindrical coordinates and evaluate it.

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