Question

Four equal Circle, each of radius a units, touch each other. show that the area between them is 6/7 a² sq units ​

Answer 1

$Radius \: of \: Circle = a$

$Side \: of \: Square = a + a \\ \\ = 2a$

$Required \: Area \\ \\ = Area \: of \: Square - \: \\ 4×area \: of \: Quadrant$

$= {(2a)}^{2} - 4 \times \frac{1}{4} \pi {r}^{2} \\ \\ = {4a}^{2} - \frac{22}{7} {a}^{2} \\ \\ = \frac{28 - 22}{7} {a}^{2} \\ \\ = \frac{6}{7} \: {a}^{2}$

Answer 2

Radius of a circle = a

Side of square = a + a

= 2a

Required Area

= Area of Square -

4 × area of Quadrant

$= (2a)^{2} - 4 \times \frac{1}{2}\pi \: r^{2}$

$= 4a^{2} - \frac{22}{7} a ^{2}$

$= \frac{28 - 22}{7}a^{2}$

$= \frac{6}{7} \: a^{2}$