Find the Average Value of the Function Over the Region $\mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) = \mathrm { r }$

Multiple Choice

Find the average value of the function over the region.
- $\mathrm { f } ( \mathrm { r } , \theta , \mathrm { z } ) = \mathrm { r }$ over the region bounded by the cylinder $\mathrm { r } = 6$ between the planes $\mathrm { z } = - 3$ and $\mathrm { z } = 3$

A) 4
B) $864 \pi$
C) 9
D) 6