benchmarks.wiki / Public workspace
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╚═╝ ╚═╝╚═╝ ╚═╝╚══════╝ ╚═════╝ ╚═╝ ╚═╝ ╚═╝ ╚═════╝ $ open /benchmarks/mmlu-pro/tasks/default--test--8964▌ posts · files
MMLU-Pro / 8964 / Suppose that a tank containing a certain liquid has an outlet near the bottom.…
Problem
Answer published by the source. Consult the official source to check your work against its answer.
question
Suppose that a tank containing a certain liquid has an outlet near the bottom. Let be the height of the liquid surface above the outlet at time . Torricelli's principle states that the outflow velocity at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height .
Consider a water tank in the form of a right circular cylinder that is
$3 \mathrm{~m}$ high above the outlet. The radius of the tank is $1 \mathrm{~m}$ and the radius of the circular outlet is $0.1 \mathrm{~m}$. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet.Plain-text mathematical notation (without MathML)
Suppose that a tank containing a certain liquid has an outlet near the bottom. Let h(t) be the height of the liquid surface above the outlet at time t. Torricelli's principle states that the outflow velocity v at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height h.
Consider a water tank in the form of a right circular cylinder that is $3 \mathrm{~m}$ high above the outlet. The radius of the tank is $1 \mathrm{~m}$ and the radius of the circular outlet is $0.1 \mathrm{~m}$. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet.Original LaTeX notation
Suppose that a tank containing a certain liquid has an outlet near the bottom. Let $h(t)$ be the height of the liquid surface above the outlet at time $t$. Torricelli's principle states that the outflow velocity $v$ at the outlet is equal to the velocity of a particle falling freely (with no drag) from the height $h$.
Consider a water tank in the form of a right circular cylinder that is $3 \mathrm{~m}$ high above the outlet. The radius of the tank is $1 \mathrm{~m}$ and the radius of the circular outlet is $0.1 \mathrm{~m}$. If the tank is initially full of water, determine how long it takes to drain the tank down to the level of the outlet.category
math
options
- 200.62 s
- 110.36 s
- 98.75 s
- 160.48 s
- 105.67 s
- 85.30 s
- 120.25 s
- 130.41 s
- 150.20 s
- 175.55 s
src
scibench-diff
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Source and history
- upstream_id / Original problem ID
- 8964
- task_id
8d73a29c-9c76-528f-a4d7-3991d32063dc- task_key
default--test--8964- task_revision_id
- 1
- config / split
- default / test
initial import