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doubletree by hilton hotel houston hobby airport houston tx 77061 - ECD Germany

📅 May 16, 2026 👤 scraface

May 16, 2026

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📌 A_2 = \frac{\sqrt{3}}{4} \cdot 14^2 = \frac{\sqrt{3}}{4} \cdot 196 = 49\sqrt{3} \text{ cm}^2

📌 Increase in area:

📌 \Delta A = A_2 - A_1 = 49\sqrt{3} - 36\sqrt{3} = 13\sqrt{3} \text{ cm}^2

📌 Thus, the area increases by \(\boxed{13\sqrt{3}}\) square centimeters.

📌 Question:** The radius of a sphere is tripled. By what factor does the volume increase?

📌 The volume \(V\) of a sphere with radius \(r\) is:

📌 Let the original radius be \(r\), so original volume is:

📌 V_1 = \frac{4}{3} \pi r^3

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