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MMLU-Pro / 10343 / Find the shortest path between the (x,y,z) points (0,−1,0) and (0,1,0)…

Problem

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

question

Find the shortest path between the (x,y,z)(x, y, z) points (0,−1,0)(0,-1,0) and (0,1,0)(0,1,0) on the conical surface z=1−x2+y2z=1-\sqrt{x^2+y^2}. What is the length of the path? Note: this is the shortest mountain path around a volcano.
Plain-text mathematical notation (without MathML)
Find the shortest path between the (x,y,z) points (0,−1,0) and (0,1,0) on the conical surface z=1−√(x²+y²). What is the length of the path? Note: this is the shortest mountain path around a volcano.
Original LaTeX notation
Find the shortest path between the $(x, y, z)$ points $(0,-1,0)$ and $(0,1,0)$ on the conical surface $z=1-\sqrt{x^2+y^2}$. What is the length of the path? Note: this is the shortest mountain path around a volcano.

category

physics

options

  1. $2 \sqrt{2} \sin \frac{\pi}{2 \sqrt{2}}$
  2. $2 \sqrt{2} \cos \frac{\pi}{\sqrt{2}}$
  3. $2 \pi \sin \frac{\pi}{4}$
  4. $2 \sqrt{2} \tan \frac{\pi}{2 \sqrt{2}}$
  5. $\frac{\pi}{2} \tan \frac{\pi}{2 \sqrt{2}}$
  6. $\pi \sqrt{2}$
  7. $2 \sqrt{2} \sin \frac{\pi}{\sqrt{2}}$
  8. $2 \sqrt{2} \cos \frac{\pi}{2 \sqrt{2}}$
  9. $4 \sin \frac{\pi}{4}$
  10. $2 \sqrt{2} \tan \frac{\pi}{\sqrt{2}}$

src

scibench-class

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Source and history

upstream_id / Original problem ID
10343
task_id
46280f9c-d96a-5ec5-9e88-7ccde38d6a58
task_key
default--test--10343
task_revision_id
1
config / split
default / test

Official source

initial import