Multiple choice general knowledge math & puzzles

A cylinder of radius 5 cm is inserted within a cylinder of radius 10 cm. The two cylinders have the same height of 20 cm. What is the volume of the region between the two cylinders?

  1. 100Pi

  2. 500Pi

  3. 1000Pi

  4. 1500Pi
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D Correct answer
Explanation

Volume of region between cylinders = π(R² - r²)h = π(10² - 5²)(20) = π(100 - 25)(20) = π(75)(20) = 1500π. This uses the formula for volume of a cylinder (V=πr²h) and subtracts the inner cylinder volume from the outer.

AI explanation

The volume of a cylinder is pi * r^2 * h. The outer cylinder has volume pi * 10^2 * 20 = 2000*pi, and the inner cylinder (which is removed) has volume pi * 5^2 * 20 = 500*pi. Subtracting gives the volume of the region between them: 2000*pi - 500*pi = 1500*pi.

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