Use cylindrical coordinates to evaluate $\iiint _ { T } \sqrt { x ^ { 2 } + y ^ { 2 } } d V$, where $T$ is the solid bounded by the cylinder $x ^ { 2 } + y ^ { 2 } = 1$ and the planes $z = 4$ and $z = 8$.
A) $\frac { 8 } { 3 } \pi$
B) $4 \pi$
C) $32 \pi$
D) $48 \pi$

Question

Quizplus · Accepted Answer

The integral in cylindrical coordinates is$$\iiint _ { T } \sqrt { x ^ { 2 } + y ^ { 2 } } d V = \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 1 } \int _ { 4 } ^ { 8 } r \ dz \ dr \ d	heta = \int _ { 0 } ^ { 2 \pi } \int _ { 0 } ^ { 1 } 4 r \ dr \ d	heta = \int _ { 0 } ^ { 2 \pi } 2 \ d	heta = 4 \pi.$$

Use Cylindrical Coordinates to Evaluate ∭Tx2+y2dV\iiint _ { T } \sqrt { x ^ { 2 } + y ^ { 2 } } d V∭T​x2+y2​dV

Use Cylindrical Coordinates to Evaluate $\iiint _ { T } \sqrt { x ^ { 2 } + y ^ { 2 } } d V$