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📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 A cylindrical tank with a radius of 4 meters and a height of 10 meters is filled with water. If a spherical ball with a radius of 2 meters is submerged in the tank, by how much will the water level rise?

📌 Volume of the cylindrical tank: \( V_{\text{cylinder}} = \pi \times 4^2 \times 10 = 160\pi \) cubic meters.

📌 Volume of the spherical ball: \( V_{\text{sphere}} = \frac{4}{3} \pi \times 2^3 = \frac{32}{3}\pi \) cubic meters.

📌 Rise in water level: \( \frac{V_{\text{sphere}}}{\text{Base area of cylinder}} = \frac{\frac{32}{3}\pi}{\pi \times 4^2} = \frac{32}{3 \times 16} = \frac{2}{3} \) meters.

📌 #### \(\frac{2}{3}\) meters

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