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?
Let the sides of a square paper be a.
A cylinder is formed by rolling the paper along its sides.
∴ 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=a2π
∴ Ratio =a2π:a=12π:1=1:2π
Hence, the ratio of the base radius to the side of the square is 1:2π