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can popping your toes cause arthritis - SUpost

📅 July 6, 2026 👤 scraface

Jul 06, 2026

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📌 Let the radius of the sphere be $r$. Then the radius of the hemisphere is $3r$.

📌 Compute the volume of the hemisphere:

📌 Question: A programmer designing a neural network architecture visualizes a right triangle with hypotenuse $h$ and an inscribed circle of radius $r$. If the triangles area is $A$, what is the ratio of the area of the circle to the area of the triangle in terms of $r$ and $h$?

📌 For a right triangle with inradius $r$ and hypotenuse $h$, the area can also be expressed in terms of the inradius and the semiperimeter $s$:

📌 However, using the known identity for a right triangle:

📌 But without $a$ and $b$, the cleanest expression is:

📌 Thus, the final answer in terms of given variables is:

📌 Question: A forestry engineer models a conical tree canopy with base radius $r$ and height $h$, and compares its volume to a cylindrical water reservoir of radius $2r$ and height $h$. What is the ratio of the volume of the cone to the volume of the cylinder?

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