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Home » Approximating \(\pi \approx 3.1416\): - go-checkin.com

Approximating \(\pi \approx 3.1416\): - go-checkin.com

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 s = \frac{a + b + c}{2} = \frac{5x + 6x + 7x}{2} = 9x

📌 Use Heron’s formula to find the area $ A $:

📌 A = \sqrt{s(s-a)(s-b)(s-c)} = \sqrt{9x(9x - 5x)(9x - 6x)(9x - 7x)} = \sqrt{9x(4x)(3x)(2x)} = \sqrt{216x^4} = 6x^2\sqrt{6}

📌 The radius $ r $ of the inscribed circle is given by:

📌 r = \frac{A}{s} = \frac{6x^2\sqrt{6}}{9x} = \frac{2x\sqrt{6}}{3}

📌 \boxed{\frac{2x\sqrt{6}}{3}}

📌 Question: A marine biologist is designing a conical fish shelter with a base radius of $ 2x $ units and a slant height of $ 5x $ units. What is the total lateral surface area of the cone in terms of $ \pi $ and $ x $?

📌 The lateral surface area of a cone is given by:

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