Question

A wire in the form of a circle of radius 42cm. It is bent into a square. Determine the side of the square and compare the area of the regions enclosed in the two cases.

Answer 1

Let the side of the square = s and the radius of the circle = r
The Circumference of a circle with radius r = 2πr
The Circumference of a Circle with radius 42
= 2π x 42
= 264cm
The Area of a Circle with radius r
= πr²
= π(42)²
= 5544cm²
The Circumference of the Circle
= Perimeter of the square
⇒ Perimeter of the Square = 264cm
⇒ 4s = 264cm
⇒ s = 66cm
Area of a Square with side s = 4s²
Area of a Square with side 66
= 4(66)²
= 4356cm²
Ratio of Area of the Circle to the Area of the Square
= 5544:4356
= 14:11.