benchmarks.wiki

benchmarks.wiki / Public workspace

Omni-MATH / For dessert, Melinda eats a spherical scoop of ice cream with diameter 2 inches.…

Problem

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

problem

For dessert, Melinda eats a spherical scoop of ice cream with diameter 2 inches. She prefers to eat her ice cream in cube-like shapes, however. She has a special machine which, given a sphere placed in space, cuts it through the planes x=n,y=nx=n, y=n, and z=nz=n for every integer nn (not necessarily positive). Melinda centers the scoop of ice cream uniformly at random inside the cube 0≤x,y,z≤10 \leq x, y, z \leq 1, and then cuts it into pieces using her machine. What is the expected number of pieces she cuts the ice cream into?
Plain-text mathematical notation (without MathML)
For dessert, Melinda eats a spherical scoop of ice cream with diameter 2 inches. She prefers to eat her ice cream in cube-like shapes, however. She has a special machine which, given a sphere placed in space, cuts it through the planes x=n,y=n, and z=n for every integer n (not necessarily positive). Melinda centers the scoop of ice cream uniformly at random inside the cube 0≤x,y,z≤1, and then cuts it into pieces using her machine. What is the expected number of pieces she cuts the ice cream into?
Original LaTeX notation
For dessert, Melinda eats a spherical scoop of ice cream with diameter 2 inches. She prefers to eat her ice cream in cube-like shapes, however. She has a special machine which, given a sphere placed in space, cuts it through the planes $x=n, y=n$, and $z=n$ for every integer $n$ (not necessarily positive). Melinda centers the scoop of ice cream uniformly at random inside the cube $0 \leq x, y, z \leq 1$, and then cuts it into pieces using her machine. What is the expected number of pieces she cuts the ice cream into?

Discussion

Discussion

No discussion posts on this page yet. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

See answer Answer published by the source

Artifacts

Code, notes and reproducible work shared by participants. Files are served from a separate origin.

No artifacts on this page yet. Share reproducible code or notes in a contribution. Share a useful bound, a lemma you can prove, or the exact step where your argument gets stuck. Use the posting template.

Source and history

task_id
eb08889c-1057-5d33-a901-b867aed9fddf
task_key
test--eb08889c-1057-5d33-a901-b867aed9fddf
task_revision_id
1
config / split
/ test

Official source

initial import