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📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 When the radius is doubled to 10 cm, the new volume \( V_2 \) is:

📌 V_2 = \frac{1}{3} \pi (10)^2 (12) = \frac{1}{3} \pi \times 100 \times 12 = 400\pi \text{ cm}^3

📌 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 \( h = 2r \).

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