Question

a square of diagonal 8 cm result inscribed in a circle . find the area of the region like outside the circle and inside the square

Answer 1

Dear please check the pic of square circumscribed in a circle. You should have written "Circumscribed" instead of inscribed.

Solution:
Since the square is inscribed in a circle. Therefore, it is property of circumscribed square in a circle that it's diagonal is the diameter of the circle.

Therefore, area of region = (π/4) x diameter^2
= (π/4) x 8^2
=50.265 cm^2

Area of square = (Diagonal^2)/2
= (8^2)/2 = 32 cm^2

Hence the area of the required region = 50.265 - 32
= 18.265 cm^2

Answer 2

A square of Diagonal 8 cm is inscribed in a circle.

From the above statement it is clear that radius of the circle is 4 cm.

Area of the circle = pie x r^2 = 3.14 x 4^2
= 3.14x16 = 50.24 cm^2

Area of the Square = (1/2) X Diagonal^2
= (1/2) X 8^2 = (1/2) X 64 = 32 cm^2

Area of the space outside square = 50.24 - 32 = 18.24 cm^2