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Home » Solution: The volume of a sphere with radius $ 2r $ is: - jntua results

Solution: The volume of a sphere with radius $ 2r $ is: - jntua results

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 The circumference of the containment field is $ \boxed{17\pi} $.

📌 Question: An entrepreneur designs a conical storage tank for renewable energy fluid containment, where the cone has height $ h $ and base radius $ r $. If the volume of the cone is equal to the volume of a sphere of radius $ r $, what is the value of $ \frac{h}{r} $?

📌 Solution: The volume of a cone is $ \frac{1}{3}\pi r^2 h $, and the volume of a sphere is $ \frac{4}{3}\pi r^3 $. Setting them equal:

📌 \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?

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