Question

Question 88

A square sheet of paper is converted into a cylinder by rolling it along its side. What is the ratio of the base radius to the side of the square?

Answer 1

Let the sides of a square paper be a.

A cylinder is formed by rolling the paper along its sides.

$\therefore$ Base of the cylinder is circle, so the circumference of the circle is equal to the length of each side of the square sheet.
$\Rightarrow 2\pi r=a$ [$\because$ circumference of circle $=2\pi r$]
$\therefore r=\frac{a}{2\pi }$
$\therefore$ Ratio $=\frac{a}{2\pi }:a=\frac{1}{2\pi }:1=1:2\pi$
Hence, the ratio of the base radius to the side of the square is $1:2\pi$