Four circular cardboard pieces, each of radius 7 cm are placed in such a way that each piece touches two other pieces. The area of the space enclosed by the four pieces is :

1. 42 cm²

2. 40 cm²

3. 21 cm²

4. 18 cm²

Given,

Radius = 7 cm

From figure,

Distance between centres of two touching circles = 2r = 2 × 7 = 14 cm.

So side of the square : AB = BC = CD = DA = 14 cm.

Area of square = (side)²

= (14)² = 196 cm².

At each corner of the square there is a quarter circle of radius 7 cm.

Four quarter circles together make one full circle.

Area of one full circle = πr²

= $\dfrac{22}{7}$ × 7²

= 22 × 7 = 154 cm².

Area of enclosed space = Area of square - Area of four quarter circles

= 196 - 154

= 42 cm².

Hence, option 1 is the correct option.