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Home » The inradius \( c \) of a right triangle is given by: - AMAZONAWS

The inradius \( c \) of a right triangle is given by: - AMAZONAWS

📅 March 5, 2026 👤 scraface

Mar 05, 2026

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📌 A cylinder has a height equal to its radius $r$. A cone with the same radius $r$ and height $r$ is placed inside the cylinder. Determine the ratio of the volume of the cone to the volume of the cylinder.

📌 The volume of the cylinder is given by \(V_{\text{cylinder}} = \pi r^2 h = \pi r^2 \cdot r = \pi r^3\).

📌 The volume of the cone is given by \(V_{\text{cone}} = \frac{1}{3} \pi r^2 h = \frac{1}{3} \pi r^2 \cdot r = \frac{1}{3} \pi r^3\).

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

📌 \frac{V_{\text{cone}}}{V_{\text{cylinder}}} = \frac{\frac{1}{3} \pi r^3}{\pi r^3} = \frac{1}{3}

📌 Thus, the final answer is \(\boxed{\frac{1}{3}}\).

📌 A regular tetrahedron has a side length of $s$. Determine the ratio of the volume of the tetrahedron to the volume of the sphere circumscribed around it.

📌 The volume of a regular tetrahedron with side length $s$ is given by:

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