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the strathallan rochester a doubletree by hilton hotel rochester ny - inBeat

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Now, the ratio of the volume of the nanoparticle to the volume of the carrier is:

📌 \frac{V_{\text{sphere}}}{V_{\text{hemisphere}}} = \frac{\frac{4}{3}\pi r^3}{18\pi r^3} = \frac{4}{3} \cdot \frac{1}{18} = \frac{4}{54} = \frac{2}{27}

📌 Final answer: $ \boxed{\frac{2}{27}} $

📌 Question: A 5 cm by 8 cm rectangle is inscribed in a circle. What is the circumference of the circle in centimeters? Express your answer in terms of $ \pi $.

📌 Using the Pythagorean theorem, the diagonal $ d $ is:

📌 So, the diameter of the circle is $ \sqrt{89} $ cm, and the radius is $ \frac{\sqrt{89}}{2} $ cm.

📌 The circumference of the circle is:

📌 Final answer: $ \boxed{\pi \sqrt{89}} $

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