Multiple choice

What is the farthest distance between two points on a cylinder of height 8 and radius 8?

  1. 8 5

  2. 8 2

  3. 16 5

  4. 8 3
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A Correct answer
Explanation

The greatest distance is between opposite points on the two circular rims. The horizontal separation is 2r = 16 and the vertical separation is 8, giving distance sqrt(16^2 + 8^2) = 8sqrt(5).

AI explanation

The farthest distance between two points on a cylinder is the length of the diagonal across the cylinder, found using the Pythagorean theorem with the diameter and the height. The diameter is twice the radius, giving a diameter of 2 * 8 = 16. Using the Pythagorean theorem, the distance is the square root of the sum of the squares of the height and the diameter: sqrt(8^2 + 16^2) = sqrt(64 + 256) = sqrt(320). Simplifying the square root gives sqrt(64 * 5) = 8 sqrt(5).

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