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Home » \( x = 4 \) liters. - Abu Waleed Tea

\( x = 4 \) liters. - Abu Waleed Tea

📅 March 1, 2026 👤 scraface

Mar 01, 2026

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📌 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

📌 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}

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