document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=341325>Question 341325</A>: <I><SPAN STYLE=\"word-break: break-all;\"> For her geometry project, Valerie has to cut out as many 2&#8208;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?\r<BR>\n" );
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document.write( "(a) 0 (b) 2 (c) 8 (d) 9 (e) 10 </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #244408 by </B><A HREF=/tutors/aboutme.mpl?userid=Theo><B>Theo(13342)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Theo><IMG SRC=http://www.algebra.com/images/aboutme-small.gif BORDER=0 alt=\"About Me\" VALIGN=MIDDLE></A>&nbsp;<IMG SRC=http://www.algebra.com/cgi-bin/show-face.mpl?user=Theo><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=244408\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> rectangular paper is 10 * 4.<BR>\n" );
document.write( "circles are 2 inches in diameter.<BR>\n" );
document.write( "she can get 2 circles in the 4 inch width.<BR>\n" );
document.write( "she can get 5 circles in the 10 inch length<BR>\n" );
document.write( "that makes a total of  5 * 2 = 10 circles that can fit into the paper.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "the total area of the 10 circles is 10 * pi * r^2.<BR>\n" );
document.write( "r is half the length of the diameter of each circle which makes r equal to 1.<BR>\n" );
document.write( "the formula becomes 10 * pi * (1)^2 = 10*pi*1 = 10*pi = 31.42592654 square inches.<BR>\n" );
document.write( "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.<BR>\n" );
document.write( "40 minus 31.42592654 square inches equals 8.584073464 square inches which rounds to 9 square inches.<BR>\n" );
document.write( "your answer should be selection d.<BR>\n" );
document.write( "if each circle was circumscribed by a square, then each of those squares would be 2 inches by 2 inches.<BR>\n" );
document.write( "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.   <BR>\n" );
document.write( "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.  <BR>\n" );
document.write( "this means that the 8.584073464 square inches that are left over are the minimum amount of paper that will be left over.\r<BR>\n" );
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