Question

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

• A. $\sqrt{4r^2+h^2}$
• B. $\sqrt{3r^2+h^2}$
• C. $\sqrt{4r^2-h^2}$
• D. $\sqrt{3r^2+2h^2}$

Answer 1

The correct option is A $\sqrt{4r^2+h^2}$

The longest needle that can be placed in the needle will be along the diagonal of the cylinder.
Using pythagoras theorem,
length of diagonal $=\sqrt{(2r{)}^2+h^2}==\sqrt{4r^2+h^2}$