Question

ℎ maximum possible square is inscribed in a circle of radius 5 cm. The area of the region of the

circle leaving the square is​

Answer 1

Given :- A square with maximum possible area is inscribed in a circle of radius 5 cm. The area of the region of the circle leaving the square is ?

Solution :-

→ Area of circle = π * (radius)² = 3.14 * (5)² = 3.14 * 25 = 78.5 cm².

now, we know that,

• Diameter of circle = Diagonal of square with maximum possible area inscribed in a circle .
• Diagonal of square = √2 * side .

Let us assume that, side of square is a cm.

so,

→ √2a = 5 * 2

→ √2a = 10

→ a = (10/√2) .

then,

→ Area of square = (side)² = a² = (10/√2)² = 100/2 = 50 cm².

therefore,

→ The area of the region of the circle leaving the square= Area of circle - Area of square = 78.5 - 50 = 28.5 cm² . (Ans.)