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📅 May 16, 2026 👤 scraface

May 16, 2026

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

📌 Solution: To find the shortest altitude, we first compute the area using Herons formula. The semi-perimeter is:

📌 Question: A historian discovers an ancient right triangle diagram where the hypotenuse is $ x $, and the radius of the inscribed circle is $ r $. What is the ratio of the area of the circle to the area of the triangle?

📌 The ratio of the circles area to the triangles area is:

📌 Question: An epidemiologist models a region as a rectangle measuring 5 cm by 12 cm, inscribed in a circular boundary. What is the circumference of the circle?

📌 Solution: The diagonal of the rectangle is the diameter of the circle. Using the Pythagorean theorem:

📌 Question: A triangle has side lengths of 9 cm, 12 cm, and 15 cm. What is the length of the longest altitude?

📌 The longest altitude corresponds to the shortest side (9 cm):

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