Question

The diameter of a coin is 1 cm. If four of these coins be placed on a table so that the rim of each touches that of the other two, find the area of the unoccupied space between them.

Answer 1

Given, 
Diameter of a coin = 1cm
Radius = diameter/2
            = 1/2=0.5 cm

If the centres are connected with each other creating a quadrilateral,
we will get a square of side = 1cm
So area of square = side * side
                              = 1*1
                              = 1 cm² 
In this square , we find four quadrants including the unoccupied space.
Radius of each quadrant = 1/2cm
Area of 1 quadrant = 22/7 * 1/2 * 1/2*1/4
                              = 0.196 approx. cm²
Area of 4 quadrants = 0.786 approx. cm²
Area of unoccupied space = 1cm² - 0.786 cm²
                                           = 0.214cm²
                                            =0.2 cm² (Ans)

Answer 2

When these coins are arranged on the table, they form a square of side 2cm by 2cm.

For us to get the area between these coins we must first get the area of the square formed by the coins and then the area of the four coins then get their difference.

Area of the square formed :2×2=4cm2

Area of the four coins:3.142 × 0.5 ×0.5 × 4=3.142cm2

Area unoccupied between the coins=area of square - area of the coins

4-3.142=0.858cm2

The area between the coins=0.858cm2