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Home » \( V = \pi \times 3^2 \times 10 = 90\pi \) cubic meters. - go-checkin.com

\( V = \pi \times 3^2 \times 10 = 90\pi \) cubic meters. - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Initial area:

📌 A_1 = \frac{\sqrt{3}}{4} \cdot 12^2 = \frac{\sqrt{3}}{4} \cdot 144 = 36\sqrt{3} \text{ cm}^2

📌 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?

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