Multiple choice

The longest needle that can be placed in a cylinder of radius r units and height h units is _____ (in units)

  1. $\displaystyle \sqrt{4r^{2}+h^{2}}$
  2. $\displaystyle \sqrt{3r^{2}+h^{2}}$
  3. $\displaystyle \sqrt{4r^{2}-h^{2}}$
  4. $\displaystyle \sqrt{3r^{2}+2h^{2}}$
Reveal answer Fill a bubble to check yourself
A Correct answer
Explanation

The longest needle in a cylinder is the space diagonal of the cylinder, which connects opposite points on the circular bases. By the Pythagorean theorem, the length is sqrt((2r)^2 + h^2) = sqrt(4r^2 + h^2).

AI explanation

The longest needle that can fit inside a cylinder corresponds to the length of its space diagonal. The space diagonal of a cylinder is calculated using the Pythagorean theorem with the diameter of the base and the height of the cylinder. The diameter is 2r, so the square of the diagonal length is (2r)^2 + h^2 = 4r^2 + h^2. Therefore, the maximum length of the needle is the square root of (4r^2 + h^2).

Keep practicing — related questions