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Home » Remaining mass: \( 128 imes \left(rac12 - RTA

Remaining mass: \( 128 imes \left(rac12 - RTA

📅 May 9, 2026 👤 scraface

May 09, 2026

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📌 V = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3

📌 The scaled cone has dimensions \( kr \) and \( 2kr \), so its volume \( V_k \) is:

📌 V_k = \frac{1}{3} \pi (kr)^2 (2kr) = \frac{1}{3} \pi k^2 r^2 \cdot 2kr = \frac{2}{3} \pi k^3 r^3

📌 The ratio of the original volume to the scaled volume is:

📌 \frac{V}{V_k} = \frac{\frac{2}{3} \pi r^3}{\frac{2}{3} \pi k^3 r^3} = \frac{1}{k^3}

📌 Thus, the ratio is \(\boxed{\frac{1}{k^3}}\).

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