document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=987649>Question 987649</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose the side length of a cube is x = 11 cm. If x changes by an amount &#948;x = 0.01 cm, what is the corresponding approximate change in the volume of the cube &#948;V?\r<BR>\n" );
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document.write( "THANK YOU :-)<BR>\n" );
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document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #608373 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=608373\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> V = x^3 ... start with the volume of a cube formula\r<BR>\n" );
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document.write( "dV/dx = 3x^2 ... apply the derivative with respect to x\r<BR>\n" );
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document.write( "dV = 3x^2*dx\r<BR>\n" );
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document.write( "dV = 3*11^2*0.01 ... plug in x = 11 and dx = 0.01\r<BR>\n" );
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document.write( "dV = 3.63\r<BR>\n" );
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document.write( "If the change in x is 0.01 cm, then the approximate change in volume is <font color=\"red\">3.63 cubic cm</font>\r<BR>\n" );
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document.write( "Alternative non-calculus based way to do it\r<BR>\n" );
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document.write( "Original Volume:<BR>\n" );
document.write( "V = x^3<BR>\n" );
document.write( "V = 11^3<BR>\n" );
document.write( "V = 1,331\r<BR>\n" );
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document.write( "Say the side length is x=11+0.01 = 11.01 now. That makes the volume become<BR>\n" );
document.write( "V = 11.01^3<BR>\n" );
document.write( "V = 1,334.633301\r<BR>\n" );
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document.write( "The difference in the two volumes is <BR>\n" );
document.write( "1,334.633301 - 1,331 = 3.63330099999984 which is approximately 3.63 that we got before\r<BR>\n" );
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document.write( "The same applies if you did x = 11-0.01 = 10.99 (the only real difference is that the result of the subtraction would be -3.63, but the absolute value of that leads to the same result) </SPAN>\n" );
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