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Home » \( x + y = 12 \) - AIKO, infinite ways to autonomy.

\( x + y = 12 \) - AIKO, infinite ways to autonomy.

📅 May 3, 2026 👤 scraface

May 03, 2026

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📌 The circumference $ C $ of the circle is given by $ C = 2\pi r $. Substituting the value of $ r $:

📌 C = 2\pi (4\sqrt{2}) = 8\sqrt{2}\pi.

📌 Thus, the circumference of the circle is $ oxed{8\sqrt{2}\pi} $.

📌 Question: A science fair judge is evaluating a student's model of a planet, shaped like a sphere with radius $ 2r $, and a supporting half-sphere with radius $ r $. What is the ratio of the volume of the planet to the volume of the half-sphere?

📌 Solution: The volume of a sphere with radius $ 2r $ is:

📌 V_{ ext{sphere}} = rac{4}{3}\pi (2r)^3 = rac{4}{3}\pi (8r^3) = rac{32}{3}\pi r^3.

📌 The volume of a hemisphere with radius $ r $ is half the volume of a full sphere:

📌 V_{ ext{hemisphere}} = rac{1}{2} \cdot rac{4}{3}\pi r^3 = rac{2}{3}\pi r^3.

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