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Home » The prime factorization of 1000 is: - All Square Golf

The prime factorization of 1000 is: - All Square Golf

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 Each gives a perfect square divisible by 4: $4, 16, 36, 64, 100, 144, 196$.

📌 Solution: Consider any four consecutive integers: $n, n+1, n+2, n+3$.

📌 Solution: Let the side length of the square be $ s $. The diagonal of a square divides it into two congruent right triangles, and the relationship between the side length and the diagonal is given by the Pythagorean theorem:

📌 Question: A square is inscribed in a circle with radius 5 cm. What is the number of centimeters in the perimeter of the square?

📌 Question: A triangle has sides of lengths 13 cm, 14 cm, and 15 cm. What is the length of the shortest altitude?

📌 Solution: To find the shortest altitude, we first compute the area using Herons formula. Let the sides be $ a = 13 $, $ b = 14 $, $ c = 15 $. The semi-perimeter is:

📌 Question: A right circular cylinder is inscribed in a sphere of radius 10 cm. If the height of the cylinder is equal to its diameter, what is the volume of the cylinder in cubic centimeters?

📌 Solution: Let the radius of the cylinder be $ r $ and its height be $ h = 2r $. The cylinder is inscribed in a sphere of radius 10, so the diagonal from the center of the sphere to the top rim of the cylinder forms a right triangle with legs $ r $ and $ r $, and hypotenuse equal to the radius of the sphere, 10 cm.

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