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Home » We proceed as follows for one fixed $ i $: - Blask

We proceed as follows for one fixed $ i $: - Blask

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 New side length is \(12 + 2 = 14\) cm, so the new area \(A_2\) is:

📌 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:

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