Question

A circular coin of radius 1 cm rolls around the inside of a square without slipping, always touching the boundary of the square.
When it returns to where it started, the coin has performed exactly one whole revolution.
In centimetres, what is the side length of the square ?

Answer 1

Answer:

A circular coin of radius 1 cm rolls around the inside of a square without slipping, always touching the boundary of the square.

When it returns to where it started, the coin has performed exactly one whole revolution.

In centimetres, what is the side length of the square ?

The length of the side of the square is 1.571 cm

Step-by-step explanation:

If the coin rolled around the inside of the square in one revolution, that means that the circumference of the circle is equal to the perimeter of the square.

Calculate the circumference of the coin:

Circumference = π × Diameter

                       = 3.142 × 2 cm

                       = 6.284 cm²

This is the circumference of the circle and is the same as the perimeter of the square

Find the side of a square with perimeter of 6.284cm² :

Formula for Perimeter of a square = 2 ( L + L )

                                      6.284cm²   = 2 ( L + L )

                                      2L = 6.284/2

                                       2 L = 3.142

                                         L = 1.571 cm

The length of this square thus is 1.571 cm