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Home » The area \( A \) of an equilateral triangle with side \( s \) is given by: - Network4

The area \( A \) of an equilateral triangle with side \( s \) is given by: - Network4

📅 May 20, 2026 👤 scraface

May 20, 2026

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📌 5**Question:** A biomimetic metabolic engineering researcher is modeling a spherical cell with radius \( r \) units and a cylindrical nutrient chamber with radius \( r \) units and height \( 3r \) units. What is the ratio of the volume of the sphere to the volume of the cylinder?

📌 The volume \( V_s \) of a sphere with radius \( r \) is given by:

📌 V_s = \frac{4}{3} \pi r^3

📌 The volume \( V_c \) of a cylinder with radius \( r \) and height \( 3r \) is:

📌 V_c = \pi r^2 \cdot 3r = 3\pi r^3

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

📌 \frac{V_s}{V_c} = \frac{\frac{4}{3} \pi r^3}{3\pi r^3} = \frac{4}{3} \cdot \frac{1}{3} = \frac{4}{9}

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