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Home » This grows without bound, so there is no horizontal asymptote. - Silent Sales Machine

This grows without bound, so there is no horizontal asymptote. - Silent Sales Machine

📅 March 10, 2026 👤 scraface

Mar 10, 2026

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📌 r = \frac{a}{2}

📌 The volume of the sphere is given by the formula:

📌 V_{\text{sphere}} = \frac{4}{3} \pi r^3 = \frac{4}{3} \pi \left( \frac{a}{2} \right)^3 = \frac{4}{3} \pi \frac{a^3}{8} = \frac{\pi a^3}{6}

📌 Now, the ratio of the volume of the sphere to the volume of the cube is:

📌 \text{Ratio} = \frac{V_{\text{sphere}}}{V_{\text{cube}}} = \frac{\frac{\pi a^3}{6}}{a^3} = \frac{\pi}{6}

📌 Thus, the ratio of the volume of the sphere to the volume of the cube is \(\boxed{\frac{\pi}{6}}\).

📌 An equilateral triangle has a side length of \( s \) units. The triangle is circumscribed about a circle. What is the ratio of the area of the circle to the area of the triangle?

📌 The area \( A_{\text{triangle}} \) of an equilateral triangle with side length \( s \) is:

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