document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1199855>Question 1199855</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Express the surface area of S of a cube as a function of its volume V.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #833882 by </B><A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><B>math_tutor2020(3816)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=math_tutor2020><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=833882\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> <font color=black size=3><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x ALIGN=MIDDLE  ALT=\"x\"   DISABLED_style= \"max-width:90%; height:auto;\" > = side length of the cube\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%2Ax%2Ax+=+x%5E3 ALIGN=MIDDLE  ALT=\"V+=+x%2Ax%2Ax+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > = volume of the cube of side length x\r<BR>\n" );
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document.write( "Solve for x<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+x%5E3 ALIGN=MIDDLE  ALT=\"V+=+x%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x+=+root%283%2CV%29 ALIGN=MIDDLE  ALT=\"x+=+root%283%2CV%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Surface area:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6x%5E2 ALIGN=MIDDLE  ALT=\"S+=+6x%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%28+root%283%2CV%29+%29%5E2 ALIGN=MIDDLE  ALT=\"S+=+6%28+root%283%2CV%29+%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Substitution using the equation above.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2 ALIGN=MIDDLE  ALT=\"S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube roots involve exponents of 1/3\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%2AV%5E%282%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"S+=+6%2AV%5E%282%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" > Apply the rule (a^b)^c = a^(b*c)\r<BR>\n" );
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document.write( "The last equation is the same as typing out S = 6*V^(2/3)\r<BR>\n" );
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document.write( "An example:<BR>\n" );
document.write( "We have a cube with side length x = 4<BR>\n" );
document.write( "volume = V = x^3 = 4^3 = 64 cubic units<BR>\n" );
document.write( "surface area = S = 6x^2 = 6*4^2 = 96 square units\r<BR>\n" );
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document.write( "Using the formula we just found,<BR>\n" );
document.write( "S = 6*V^(2/3)<BR>\n" );
document.write( "S = 6*64^(2/3)<BR>\n" );
document.write( "S = 96\r<BR>\n" );
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document.write( "Answer:\r<BR>\n" );
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document.write( "Either of the following<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%28+root%283%2CV%29+%29%5E2 ALIGN=MIDDLE  ALT=\"S+=+6%28+root%283%2CV%29+%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2 ALIGN=MIDDLE  ALT=\"S+=+6%28+V%5E%281%2F3%29%5E%22%22+%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "or<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=S+=+6%2AV%5E%282%2F3%29%5E%22%22 ALIGN=MIDDLE  ALT=\"S+=+6%2AV%5E%282%2F3%29%5E%22%22\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Other forms are possible.<BR>\n" );
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