Question

When a wire is bent in the form of a square, then the area enclosed by it is 5929 cm2. If wire is bent into the form of a circle, then what will be the area enclosed by the wire?

• A. 7546 sq.cm
• B. 8542 sq.cm
• C. 7632 sq.cm
• D. 6954 sq.cm

Answer 1

Answer:

A. 7546 sq.cm

Solution:

Given:

Area of square = 5929 cm²

Concept:

The length of the wire stays the same, which is the perimeter of the square and also the circumference of the circle.

Solution:

⇒ Side of square = √5929 = 77 cm

⇒ Perimeter of square = 4 × 77 = 308 cm

⇒ This becomes the circumference of the circle, so, radius of circle = Circumference / (2π) = 308 / (2 × 3.14) = 49 cm

⇒ Area of circle = πr² = 3.14 × 49 × 49 = 7546 cm²

Therefore, the area enclosed by the wire when it is bent into a circle is 7546 cm².