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

1 Answer
Nov 30, 2015

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