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us teacher appreciation day 2025 freebies - Feedz API

📅 May 17, 2026 👤 scraface

May 17, 2026

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

📌 The volume of a cube is $ V_{\text{cube}} = s^3 $. For the cube, $ s = 6r $, so:

📌 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 $.

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