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MMLU-Pro / 8531 / The temperature at the point (x,y,z) in a substance with conductivity…

Problem

Answer published by the source. Consult the official source to check your work against its answer.

question

The temperature at the point (x,y,z)(x, y, z) in a substance with conductivity K=6.5K=6.5 is u(x,y,z)=2y2+2z2u(x, y, z)=2 y^2+2 z^2. Find the rate of heat flow inward across the cylindrical surface y2+z2=6y^2+z^2=6, 0≤x≤40 \leqslant x \leqslant 4
Plain-text mathematical notation (without MathML)
The temperature at the point (x,y,z) in a substance with conductivity K=6.5 is u(x,y,z)=2y²+2z². Find the rate of heat flow inward across the cylindrical surface y²+z²=6, 0≤x≤4
Original LaTeX notation
The temperature at the point $(x, y, z)$ in a substance with conductivity $K=6.5$ is $u(x, y, z)=2 y^2+2 z^2$. Find the rate of heat flow inward across the cylindrical surface $y^2+z^2=6$, $0 \leqslant x \leqslant 4$

category

math

options

  1. $800\pi$
  2. $1504\pi$
  3. $1248\pi$
  4. $1560\pi$
  5. $960\pi$
  6. $1104\pi$
  7. $1320\pi$
  8. $1400\pi$
  9. $1040\pi$
  10. $984\pi$

src

scibench-calculus

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Source and history

upstream_id / Original problem ID
8531
task_id
3ec20ed4-16f1-597f-9d95-11e22bbf9e1b
task_key
default--test--8531
task_revision_id
1
config / split
default / test

Official source

initial import