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Fotos auf art2hotel.com. - Abbey Badges

📅 February 27, 2026 👤 scraface

Feb 27, 2026

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📌 Solution: The volume of a cone is given by $ V_{\text{cone}} = \frac{1}{3}\pi r^2 h $. Substituting $ h = 2r $, we get:

📌 V_{\text{cone}} = \frac{1}{3} \pi r^2 (2r) = \frac{2}{3} \pi r^3

📌 The volume of a sphere is $ V_{\text{sphere}} = \frac{4}{3} \pi r^3 $.

📌 The ratio of the volume of the cone to the volume of the sphere is:

📌 \frac{V_{\text{cone}}}{V_{\text{sphere}}} = \frac{\frac{2}{3} \pi r^3}{\frac{4}{3} \pi r^3} = \frac{2}{4} = \frac{1}{2}

📌 Thus, the ratio is $ \boxed{\frac{1}{2}} $.

📌 Question: A science administrator is reviewing a grant proposal involving a cylindrical tank with radius $ 3r $ and height $ 4r $, and a cube with edge length $ 6r $. What is the ratio of the volume of the cylinder to the volume of the cube?

📌 Solution: The volume of a cylinder is $ V_{\text{cyl}} = \pi r^2 h $. For the cylinder, $ r = 3r $ and $ h = 4r $, so:

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