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Home » The Shortcut No Excel Pro Was Told About (Proven to Save Hours) - AIKO, infinite ways to autonomy.

The Shortcut No Excel Pro Was Told About (Proven to Save Hours) - AIKO, infinite ways to autonomy.

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 The factor of increase is:

📌 \frac{V_2}{V_1} = \frac{400\pi}{100\pi} = 4

📌 Thus, the volume increases by a factor of:

📌 Question:** A cylinder has a height equal to twice its radius. If the height is increased by 50% and the radius is decreased by 20%, what is the ratio of the new volume to the original volume?

📌 Let the original radius be \( r \), so the original height is \( h = 2r \).

📌 Original volume:

📌 V_1 = \pi r^2 h = \pi r^2 (2r) = 2\pi r^3

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收益 = 0 → 年化收益率 = 0%
假设第一年涨25% → 1.25, 第二年按预期下跌20% → 0.8，复合：
\[ (1.25 \times 0.8)^1 = 1.00 \Rightarrow r = 0\% \]
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