benchmarks.wiki / Public workspace
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╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--8580▌ posts · files
MMLU-Pro / 8580 / Water drips out of a hole at the vertex of an upside down cone at a rate of 3…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
Water drips out of a hole at the vertex of an upside down cone at a rate of 3 cm^3 per minute. The cone’s height and radius are 2 cm and 1 cm, respectively. At what rate does the height of the water change when the water level is half a centimeter below the top of the cone? The volume of a cone is V = (π/3)*r^2*h, where r is the radius and h is the height of the cone.
category
math
options
- −28/(3π) cm/min
- −8/(3π) cm/min
- −24/(3π) cm/min
- −48/π cm/min
- −12/(3π) cm/min
- −4/(3π) cm/min
- −32/(3π) cm/min
- −20/(3π) cm/min
- −40/(3π) cm/min
- −16/(3π) cm/min
src
ori_mmlu-college_mathematics
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Source and history
- upstream_id / Original problem ID
- 8580
- task_id
897656d1-f4f6-587a-9bc6-27005d17e1da- task_key
default--test--8580- task_revision_id
- 1
- config / split
- default / test
initial import