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AIME 2024 / AIME 2024 train bb64a047-3645-5196-82a1-d7817da20997

Problem

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Problem

Let

\mathcal{B}

be the set of rectangular boxes with surface area

54

and volume

23

. Let

r

be the radius of the smallest sphere that can contain each of the rectangular boxes that are elements of

\mathcal{B}

. The value of

r^2

can be written as $\rac{p}{q}$ , where

p

and

q

are relatively prime positive integers. Find

p+q

Plain-text mathematical notation (without MathML)

Let B be the set of rectangular boxes with surface area 54 and volume 23. Let r be the radius of the smallest sphere that can contain each of the rectangular boxes that are elements of B. The value of r² can be written as $\rac{p}{q}$, where p and q are relatively prime positive integers. Find p+q.

Original LaTeX notation

Let $\mathcal{B}$ be the set of rectangular boxes with surface area $54$ and volume $23$. Let $r$ be the radius of the smallest sphere that can contain each of the rectangular boxes that are elements of $\mathcal{B}$. The value of $r^2$ can be written as $\rac{p}{q}$, where $p$ and $q$ are relatively prime positive integers. Find $p+q$.

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Source and history

task_id: bb64a047-3645-5196-82a1-d7817da20997
task_key: default--train--bb64a047-3645-5196-82a1-d7817da20997
task_revision_id: 2
config / split: default / train

Official source

initial import