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MMLU-Pro / 9336 / Find the ratio of the radius R to the height H of a right-circular cylinder…

Problem

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

question

Find the ratio of the radius RR to the height HH of a right-circular cylinder of fixed volume VV that minimizes the surface area AA.
Plain-text mathematical notation (without MathML)
Find the ratio of the radius R to the height H of a right-circular cylinder of fixed volume V that minimizes the surface area A.
Original LaTeX notation
Find the ratio of the radius $R$ to the height $H$ of a right-circular cylinder of fixed volume $V$ that minimizes the surface area $A$.

category

physics

options

  1. $\frac{1}{2}$ $H$
  2. $\frac{1}{4}$ $H$
  3. $\frac{3}{2}H$
  4. $\frac{2}{3}H$
  5. $2H$
  6. $\sqrt{2}H$
  7. $3H$
  8. $H$
  9. $\frac{H}{\sqrt{3}}$
  10. $\frac{1}{\sqrt{2}}H$

src

scibench-class

Discussion

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Source and history

upstream_id / Original problem ID
9336
task_id
518cfb7b-ff97-56c1-8799-5e42aa6580ce
task_key
default--test--9336
task_revision_id
1
config / split
default / test

Official source

initial import