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Home » d = \frac20253 = 675 - inBeat

d = \frac20253 = 675 - inBeat

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 5Question: A right triangle has legs of lengths $ a $ and $ b $, and a hypotenuse of length $ c $. If the triangles inradius is $ r $, what is the ratio of the area of the incircle to the area of the triangle?

📌 Question: A patent attorney is analyzing a mechanical design involving a cylinder and a cone with equal base radii and equal heights. If the volume of the cone is $ V $, what is the ratio of the surface area of the cone (excluding the base) to the surface area of the cylinder?

📌 Solution: Let the radius be $ r $ and the height be $ h $.

📌 Question: A philosopher of science is modeling a theoretical space as a regular tetrahedron. If each edge has length $ a $, what is the volume of the tetrahedron and the radius of its inscribed sphere?

📌 The radius $ r $ of the inscribed sphere (inradius) is:

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