Question

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 side.

∴ Base of the cylinder is circle, so the circumference of the circle is equal to the length of each side of the square sheet.

⇒ 2πr = a  ...[∵ Circumference of circle = 2πr]

∴ `r = a/(2pi)`

∴ Ratio = `a/(2pi) : a`

= `1/(2pi) : 1`

= 1 : 2π

Hence, the ratio of the base radius to the side of the square is 1 : 2π.