Question

A square of diagonal 8 cm is inscribed in a circle. Find the area of the region lying outside the circle and inside the square. 

Answer 1

Let the side of a square be a and the radius of circle be r.

Given that, length of diagonal of square = 8 cm

⇒ `asqrt2 = 8`

⇒ `a = 4sqrt2` cm

Now, Diagonal of a square = Diameter of a circle

⇒ Diameter of circle = 8

⇒ Radius of circle = r = `"Diameter"/2`

⇒ `r = 8/2 = 4` cm

∴ Area of circle = `pir^2 = pi(4)^2`

= `16pi xx cm^2`

and Area of square = `a^2 = (4sqrt2)^2`

= 32 cm²