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

Answer: the radius of the circle is 14 cm. :)

Explanation:

To find,

The radius of the circle.

Solution,

The radius of the circle will be 14 cm.

We can easily solve this problem by following the given steps.

According to the question,

Length of a rectangular wire = 32 cm

The breadth of a rectangular wire = 12 cm

This wire is bent into the shape of a circle.

So,

The perimeter of the rectangle = Circumference of the circle

We know the formula for the perimeter of a rectangle is as follows:

P = 2(Length+Breadth)

P = 2(32+12) cm

P = 2(44) cm

P = 88 cm

We know that the formula to find the circumference of the circle is given as follows:

C =

2πr = 88 cm

2×22r/7 = 88

44r/7 = 88

Using the cross multiplication method,

44r = (88×7)

r = (88×7)/44

r = (2×7) cm

r = 14 cm

Hence, 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.