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📅 May 13, 2026 👤 scraface

May 13, 2026

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📌 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

📌 After tripling the radius, new radius is \(3r\), so new volume \(V_2\) is:

📌 V_2 = \frac{4}{3} \pi (3r)^3 = \frac{4}{3} \pi \cdot 27r^3 = 27 \cdot \frac{4}{3} \pi r^3 = 27V_1

📌 Thus, the volume increases by a factor of \(\boxed{27}\).

📌 Question:** In a right triangle, one leg is 6 cm and the hypotenuse is 10 cm. Find the length of the shortest altitude.

📌 Let the triangle have legs \(a = 6\) cm, hypotenuse \(c = 10\) cm. Use the Pythagorean theorem to find the other leg \(b\):

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