Question

The difference between the area of the outer and the inner square of a circle is 63 cm² and O is the centre of the circle. Find the area of the circle.

Answer 1

on observation;

for bigger square,

diameter of circle = side of outer square

side of outer square = 2a

area = (side)² = (2a)² = 4a²

for smaller square,

two radii act as diagonals and hence the radii are perpendicular

so, in one quadrant of the smaller square

(side)² = a² + a² ... (Pythagorean theorem)

area = 2a²

now,

difference between areas of two squares

= 4a² - 2a²

= 2a² = 63 cm²

=> a² = $\frac{63}{2}$

now,

area of circle

= πa²

= $(\frac{22}{7})(\frac{63}{2})$

= 11 x 9

= 99 cm²

Hence, area of the circle is 99 cm².