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Play Great Games Online: Top Ranked Picks for Endless Fun & Challenge - Treasure Valley Movers

📅 April 17, 2026 👤 scraface

Apr 17, 2026

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📌 #### 104.17**Question:** A cylinder has a height equal to the diameter of its base. If the radius of the base is \( r \) units, what is the ratio of the volume of the cylinder to the volume of a sphere with radius \( r \)?

📌 The volume \( V_{\text{cylinder}} \) of a cylinder with height \( h = 2r \) and base radius \( r \) is given by the formula:

📌 \[ V_{\text{cylinder}} = \pi r^2 h = \pi r^2 (2r) = 2\pi r^3. \]

📌 The volume \( V_{\text{sphere}} \) of a sphere with radius \( r \) is given by:

📌 \[ V_{\text{sphere}} = \frac{4}{3} \pi r^3. \]

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

📌 \[ \frac{V_{\text{cylinder}}}{V_{\text{sphere}}} = \frac{2\pi r^3}{\frac{4}{3} \pi r^3} = \frac{2 \cdot 3}{4} = \frac{6}{4} = \frac{3}{2}. \]

📌 Thus, the ratio is \(\boxed{\frac{3}{2}}\).

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