Question

The length and breadth of a rectangular wire are 32 cm and 12 cm. It is bent into the shape of a circle. Find the radius of the circle. (Take p = 3.14)

Answer 1

The perimeter of the circle formed by bending the rectangular wire will be equal to the length of the wire.

Perimeter of the circle = Length of the wire

2πr = 2(l+b) where r is the radius of the circle, l is the length of the wire, and b is the breadth of the wire.

Substituting the given values, we get:

2 x 3.14 x r = 2(32 + 12)

6.28r = 88

r = 14 cm

Therefore, the radius of the circle is 14 cm.

Answer 2

14.01 cm

Explanation:

The length of the wire is equal to the perimeter of the rectangle. So, the length of the wire is:

• 2 × (32 + 12) = 88 cm

When this wire is bent into a circle, its length becomes equal to the circumference of the circle. The formula for the circumference of a circle is:

(let r = radius)

• 2 × π × r

So, we can write:

• 2 × π × r = 88

Solving for r, we get:

• r = 88 ÷ (2 × π) = 14.01 cm

So, the exact value of the radius of the circle formed by bending this rectangular wire is 14.01 cm.