Question 341325: For her geometry project, Valerie has to cut out as many 2‐inch diameter circles as she can from a rectangular sheet of paper 10 inches by 4 inches. To the nearest square inch, what is the least amount of paper she could have left?
(a) 0 (b) 2 (c) 8 (d) 9 (e) 10
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! rectangular paper is 10 * 4.
circles are 2 inches in diameter.
she can get 2 circles in the 4 inch width.
she can get 5 circles in the 10 inch length
that makes a total of 5 * 2 = 10 circles that can fit into the paper.
the area of each circle is given by the formula pi*r^2 where r is the radius and pi is the constant of 3.14..... that should be stored in your calculator.
the total area of the 10 circles is 10 * pi * r^2.
r is half the length of the diameter of each circle which makes r equal to 1.
the formula becomes 10 * pi * (1)^2 = 10*pi*1 = 10*pi = 31.42592654 square inches.
the area of the rectangular piece of paper is equal to length * width which is equal to 4 * 10 which is equal to 40 square inches.
40 minus 31.42592654 square inches equals 8.584073464 square inches which rounds to 9 square inches.
your answer should be selection d.
if each circle was circumscribed by a square, then each of those squares would be 2 inches by 2 inches.
the area of the circumscribing square would be 4 square inches and the area for the circumscribed circle would be 3.141592654 square inches which would result in a difference of .8584073464 square inches for each circle.
since 10 * .8584073464 is equal to 8.584073464, this means that you cannot get more than 10 circles in the 10 by 4 rectangular piece of paper.
this means that the 8.584073464 square inches that are left over are the minimum amount of paper that will be left over.
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