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Home » The radius \( r \) of the inscribed sphere in a regular tetrahedron is: - Crosslake

The radius \( r \) of the inscribed sphere in a regular tetrahedron is: - Crosslake

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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r = rac{a + b - c}{2}
First, calculate the hypotenuse $ c $ using the Pythagorean theorem:
c = \sqrt{5^2 + 12^2} = \sqrt{25 + 144} = \sqrt{169} = 13 ext{ cm}
Now substitute into the formula for $ r $:
r = rac{5 + 12 - 13}{2} = rac{4}{2} = 2 ext{ cm}
Thus, the radius of the inscribed circle is $ oxed{2} $ cm.
Question: A square with side length $ 8 $ cm is inscribed in a circle....
Solution: The diagonal of the square is the diameter of the circle. Fo...
d = s\sqrt{2}
Substituting $ s = 8 $:

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