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📅 May 18, 2026 👤 scraface

May 18, 2026

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📌 Question:** A virologist models a viral capsid as a sphere with radius \(3\) nm. Nearby, a cylindrical nanoparticle with height \(6\) nm and base radius \(2\) nm is used in therapy. What is the ratio of the volume of the sphere to the volume of the cylinder?

📌 The volume \(V_s\) of the sphere is given by:

📌 \[ V_s = \frac{4}{3}\pi r^3 \]

📌 where \(r = 3\) nm:

📌 \[ V_s = \frac{4}{3}\pi (3)^3 = \frac{4}{3}\pi \times 27 = 36\pi \]

📌 The volume \(V_c\) of the cylinder is given by:

📌 \[ V_c = \pi r^2 h \]

📌 where \(r = 2\) nm and \(h = 6\) nm:

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