The Temperature at the Point $( x , y , z )$

Multiple Choice

The temperature at the point $( x , y , z )$ in a substance with conductivity $K = 4$ is $u ( x , y , z ) = 2 x ^ { 2 } + 2 y ^ { 2 }$ .

Find the rate of heat flow inward across the cylindrical $y ^ { 2 } + z ^ { 2 } = 2,0 \leq x \leq 7$ .
Select the correct answer.

A) 224
B) $234 \pi$
C) $244 \pi$
D) $264 \pi$
E) $224 \pi$