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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?
Solution
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.
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