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Home » \lim_n o \infty c_n = 0 - Nelissen Grade advocaten

\lim_n o \infty c_n = 0 - Nelissen Grade advocaten

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 Thus, the ratio of the area of the circle to the area of the triangle is \(\boxed{\frac{\pi \sqrt{3}}{9}}\).

📌 A regular tetrahedron has a side length of \( b \) units. What is the ratio of the volume of the inscribed sphere to the volume of the tetrahedron?

📌 The volume \( V_{\text{tetrahedron}} \) of a regular tetrahedron with side length \( b \) is:

📌 V_{\text{tetrahedron}} = \frac{b^3}{6\sqrt{2}}

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

📌 r = \frac{b \sqrt{6}}{12}

📌 The volume \( V_{\text{sphere}} \) of the inscribed sphere is:

📌 V_{\text{sphere}} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \left( \frac{b \sqrt{6}}{12} \right)^3 = \frac{4}{3} \pi \frac{6\sqrt{6} b^3}{1728} = \frac{\pi \sqrt{6} b^3}{864}

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