Question

A steel wire, when bent in the form of a square, encloses an area of 121 sq cm. The same wire

is bent, in the form of a circle. Find the area of the circle.

​

Answer 1

A = 49
`\pi`

Explanation:

First, we need to find the length of the wire. We can calculate this because we are given the area of the square, so we can work backwards.

Use the area formula and plug in the numbers:

A = s²

121 = s²

11 = s

We can calculate the length of the wire by multiplying 11 by 4, which is 44.

Now, we know the circumference of the circle is 44 units because that is how long the wire is.

We can work backwards again to find the radius, using the circumference formula:

C = 2
`\pi`r

44 = 2
`\pi`r

22 =
`\pi`r

7 = r

Now, we can find the area of the circle:

A =
`\pi`r²

A =
`\pi`(7)²

A = 49
`\pi`