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Home » You Won’t Believe What Exegol Reveals About Ancient Prophecies! - Upplift

You Won’t Believe What Exegol Reveals About Ancient Prophecies! - Upplift

📅 February 28, 2026 👤 scraface

Feb 28, 2026

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📌 From Despair to Fame: Ultra Despair Girls Shock the World With Their Raw PainQuestion: A palynologist models a pollen grain as a perfect sphere with radius $ r $, while a spore is modeled as a hemisphere with radius $ 3r $. What is the ratio of the surface area of the pollen grain to the surface area of the spore, including its flat base?

📌 Solution: The surface area of a sphere is $ 4\pi r^2 $. For the pollen grain, this is $ 4\pi r^2 $. The surface area of a hemisphere includes the curved surface ($ 2\pi (3r)^2 $) and the flat circular base ($ \pi (3r)^2 $), so total surface area is $ 2\pi (9r^2) + \pi (9r^2) = 18\pi r^2 + 9\pi r^2 = 27\pi r^2 $. The ratio is:

📌 \frac{4\pi r^2}{27\pi r^2} = \frac{4}{27}

📌 Thus, the ratio of the surface area of the pollen grain to the spore is $ \boxed{\dfrac{4}{27}} $.

📌 Question: A science administrator is reviewing a proposal involving a circular containment field shaped as a circle circumscribed around a rectangle representing a research lab layout, where the rectangle measures 8 meters by 15 meters. What is the circumference of the containment field in meters? Express your answer in terms of $ \pi $.

📌 Solution: The diagonal of the rectangle is the diameter of the circumscribed circle. Using the Pythagorean Theorem:

📌 \text{Diagonal} = \sqrt{8^2 + 15^2} = \sqrt{64 + 225} = \sqrt{289} = 17 \text{ meters}

📌 So, the diameter of the circle is 17 meters, and the circumference is:

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