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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:

If the square sheet of paper of side ‘a’ is rolled into a cylinder then the circumference of the circular base of the cylinder will be equal to the length of the side of the square sheet.

Mathematically stated we get:

2πr = a

Where r = radius of the base of the cylinder

a = length of the side of the square

r = a/2π

Ratio of the base radius to the side of the square = [a/2π]/a = 1/2π = 1:2π

✦ Try This: A square sheet of paper is converted into a cylinder by rolling it along its side. What is the ratio of the curved surface area of the cylinder to the area of the square sheet from which the cylinder is formed?

If the square sheet of paper of side ‘a’ is rolled into a cylinder then the circumference of the circular base of the cylinder will be equal to the length of the side of the square sheet.

Mathematically stated we get:

2πr = a

Where r = radius of the base of the cylinder

a = length of the side of the square

r = a/2π

The length or height of the cylinder formed will also be equal to ‘a’

The curved surface area of the cylinder is 2πrh= 2π × a/2π × a = a²

The ratio of the curved surface area of the cylinder to the area of the square sheet = a²/a² = 1

☛ Also Check: NCERT Solutions for Class 8 Maths Chapter 11

NCERT Exemplar Class 8 Maths Chapter 11 Problem 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?

Summary:

A square sheet of paper is converted into a cylinder by rolling it along its side. The ratio of the base radius to the side of the square is 1:2π

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