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Home » \frac{3\sqrt3}2s^2 = 54\sqrt3 - Imagemakers

\frac{3\sqrt3}2s^2 = 54\sqrt3 - Imagemakers

📅 April 30, 2026 👤 scraface

Apr 30, 2026

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📌 V_{\text{cube}} = (6r)^3 = 216r^3

📌 The ratio of the cylinder's volume to the cube's volume is:

📌 \frac{V_{\text{cyl}}}{V_{\text{cube}}} = \frac{36\pi r^3}{216r^3} = \frac{36\pi}{216} = \frac{\pi}{6}

📌 Thus, the ratio is $ \boxed{\frac{\pi}{6}} $.

📌 Question: A pharmacologist is modeling a spherical drug capsule of radius $ r $ and a hemispherical cap of radius $ r $ attached to a cylindrical urodose container of height $ 2r $ and radius $ r $. What is the total volume of the composite object?

📌 Solution: The volume of a hemisphere is $ V_{\text{hemisphere}} = \frac{2}{3} \pi r^3 $.

📌 The volume of the cylinder is $ V_{\text{cyl}} = \pi r^2 h = \pi r^2 (2r) = 2\pi r^3 $.

📌 The total volume is:

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