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Home » The probability that at least one occurs is 0.58. - AssociationVoting

The probability that at least one occurs is 0.58. - AssociationVoting

📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 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:

📌 V_{\text{cyl}} = \pi (3r)^2 (4r) = \pi (9r^2)(4r) = 36\pi r^3

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