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Home » at which angle will the hexagon rotate onto itself - Imagemakers

at which angle will the hexagon rotate onto itself - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 \frac{1}{3}\pi r^2 h = \frac{4}{3}\pi r^3

📌 Divide both sides by $ \frac{1}{3}\pi r^2 $:

📌 Thus, $ \frac{h}{r} = \boxed{4} $.

📌 Question: A palynologist observes a pollen grain with a circular cross-section of diameter 10 micrometers, and inside it, a spore with a square cross-section inscribed such that its vertices touch the circumference. What is the area, in square micrometers, of the region within the circular grain but outside the square spore?

📌 Solution: The circle has radius $ 5 $ micrometers, so its area is:

📌 \pi (5)^2 = 25\pi \text{ μm}^2

📌 The square is inscribed in the circle, so its diagonal is the diameter, 10 μm. For a square, diagonal $ d = s\sqrt{2} $, so:

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