Question

A copper wire when bent in the form of a square encloses an area of `121``cm^2`. If the same wire is bent into the form of a circle, what is the area of the circle?

Answer 1

`484/pi cm^2~~154.061984913 cm^2`

Explanation:

First we need to find the length of the wire.
To do that, we should try to figure out the length of 1 side of the square

Area of a square `= (side)^2`
that means that a `(side) = sqrt(121)` if the Area of the square was 121.
therefore one side of the square would be `sqrt(121) = 11`

The Perimeter of the square would be equal to the full length of the copper wire.
Perimeter of a square `= 4(side)`

since we just found that `(side) = 11`
we can determine that the Perimeter would be `11*4 = 44`

Therefore the length of the copper wire would be `44cm` long

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If we make a circle from this wire, the length of the wire would then be the Circumference of the Circle.
Circumference of a Circle `= 2 pi (radius)`

from this we can get that `(radius) = 44/{2pi} = 22/pi`

Then, the Area of the Circle would be
Area of a Circle `= pi(radius)^2`

Since we found that `(radius) = 22/pi`
we can figure out that the Area of the Circle would be
`pi(22/pi)^2 = 484/pi ~~154.061984913` `leftarrow` answer