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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 The altitude $ h $ corresponding to base $ c = 15 $ is:

📌 Question: A meteorologist models a tornado as a right circular cone with base radius $ r $ and height $ h $. If the volume of the tornado is equal to that of a sphere of radius $ r $, what is the height $ h $ of the cone in terms of $ r $?

📌 The volume of a sphere of radius $ r $ is:

📌 The new side length is $ s = 20 + 4 = 24 $.

📌 Solution: A right triangle inscribed in a semicircle must have its hypotenuse as the diameter of the semicircle. Using the Pythagorean theorem, the hypotenuse $ c $ of the triangle with legs 5 cm and 12 cm is:

📌 Since the hypotenuse is the diameter of the semicircle, the radius is half of this:

📌 Question: A library technologist is digitizing a 17th-century manuscript containing a geometric puzzle: a triangle with side lengths 13, 14, and 15 cm. What is the radius of the circumscribed circle around this triangle?

📌 Solution: To find the radius $ R $ of the circumscribed circle of a triangle with sides $ a = 13 $, $ b = 14 $, and $ c = 15 $, we use the formula:

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