document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1122921>Question 1122921</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Write a formula that expresses the radius of a circle in cm, r, in terms of the circumference of the circle in inches, C.\r<BR>\n" );
document.write( "\n" );
document.write( "r=\r<BR>\n" );
document.write( "\n" );
document.write( "Write a formula that expresses the area of the circle in cm2, A, in terms of the radius of the circle in cm, r.\r<BR>\n" );
document.write( "\n" );
document.write( "A=\r<BR>\n" );
document.write( "\n" );
document.write( "Write a formula that expresses the area of the circle in cm2, A, in terms of the circumference of the circle in inches, C.\r<BR>\n" );
document.write( "\n" );
document.write( "A=\r<BR>\n" );
document.write( "\n" );
document.write( "Suppose the function f determines the area of the circle in cm2 given the circumference of the circle in inches, C. Write a function formula for f.\r<BR>\n" );
document.write( "\n" );
document.write( "f(C)=\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #739166 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=739166\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Write a formula that expresses the radius of a circle in cm, r, in terms of the circumference of the circle in inches, C. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for circumference of a circle is C = 2 * pi * r<BR>\n" );
document.write( "C is the circumference, r is the radius.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "if you solve this equation for r, you will get:<BR>\n" );
document.write( "r = C / (2 * pi).\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Write a formula that expresses the area of the circle in cm2, A, in terms of the radius of the circle in cm, r. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the area of a circle is A = pi * r^2.<BR>\n" );
document.write( "A is the area and r is the radius.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Write a formula that expresses the area of the circle in cm2, A, in terms of the circumference of the circle in inches, C. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the circumference of a circle C = 2 * pi * r\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the area of a circle is A = pi * r^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the formula of C = 2 * pi * r, solve for r to get r = C / (2 * pi)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "in the formula of A = pi * r^2, replace r with C / (2 * pi) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = pi * (C / (2 * pi)) ^ 2\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "Suppose the function f determines the area of the circle in cm2 given the circumference of the circle in inches, C. Write a function formula for f. \r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the function f determines the area of the circle in square centimeters, given the circumference of the circle in inches.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the circumference of the circle is C = 2 * pi * r.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "solve this formula for r to get r = C / (2 * pi)\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the formula for the area of the circle is A = pi * r^2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "replace r in this formula with C / (2 * pi) to get:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = pi * (C / (2 * pi)) ^ 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "now C is in inches and you want A in square centimeters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "the conversion factor from inches to centimeters is:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "1 inch = 2.54 centimeters\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "therefore, if the circumference is in inches, you would multiply it by 2.54 to get the equivalent value in centimeters.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "you formula for A in terms of C would become:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = pi * (C / (2 * pi) * 2.54) ^ 2.\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "this could also be written as:\r<BR>\n" );
document.write( "<BR>\n" );
document.write( "\n" );
document.write( "A = pi * (C / (2 * pi)) ^ 2 * 2.54 ^ 2.\r<BR>\n" );
document.write( "\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );