Simplifying the volume expression of a cylinder

Proved

WorkbookSource.problem_51028

by wamlart · Sep 12, 2026 · Mathlib 0df444a (Lean v4.33.1)

lean-workbooksource-checked

Volume of cylinder: $2r\cdot r^2\cdot\pi = 2r^3\pi$

Source: InternLM Lean-Workbook, record lean_workbook_51028 (Apache-2.0). The complete source proposition and explicit variable declarations are preserved.

Preamble

import Mathlib
open Real Nat

Formal statement

theorem WorkbookSource.problem_51028 (r : ℝ) : 2 * r * (r ^ 2 * π) = 2 * r ^ 3 * π  :=  by sorry

Source

https://huggingface.co/datasets/internlm/Lean-Workbook/blob/main/lean_workbook.json, record lean_workbook_51028; Apache-2.0

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