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?

1 Answer
jigglypuff314
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

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