document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=142462>Question 142462</A>: <I><SPAN STYLE=\"word-break: break-all;\"> How are surface area and volume affected when the dimension of a box is quadrupled. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #103699 by </B><A HREF=/tutors/aboutme.mpl?userid=ptaylor><B>ptaylor(2198)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=ptaylor><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=ptaylor><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=103699\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Volume(V) of a box=Length(L) times Width(W) times Height(H) or:<BR>\n" );
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document.write( "V=LWH --------------------------------------------eq1<BR>\n" );
document.write( "now if we quadruple the dimensions, we have:\r<BR>\n" );
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document.write( "V1=4L*4W*4H=64LWH--------------------------------eq2<BR>\n" );
document.write( "Substitute LWH=V from eq1 into eq2:\r<BR>\n" );
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document.write( "V1=64V<BR>\n" );
document.write( "So, when we quadruple the dimensions, the volume is increased by a factor of 64\r<BR>\n" );
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document.write( "Surface Area(SA) of a box equals Area of Top plus Area of Bottom plus Area of Front plus Area of Back plus Area of Each Side<BR>\n" );
document.write( "Area of Top plus Bottom=2LW<BR>\n" );
document.write( "Area of Front plus Back=2WH<BR>\n" );
document.write( "Area of the two Sides=2LH, so:\r<BR>\n" );
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document.write( "SA=2LW+2WH+2LH----------------------------------------eq3<BR>\n" );
document.write( "now if we quadruple the dimensions, we have:\r<BR>\n" );
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document.write( "SA1=2*4L*4W+2*4W*4H+2*4L*4H and this equals<BR>\n" );
document.write( "SA1=16(2LW)+16(2WH)+16(2LH)  from the right side, factor out 16:\r<BR>\n" );
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document.write( "SA1=16(2LW+2WH+2LH)-----------------------------------------eq4<BR>\n" );
document.write( "substitute 2LW+2WH+2LH=SA from eq3 into eq4 and we get:\r<BR>\n" );
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document.write( "SA1=16SA\r<BR>\n" );
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document.write( "So, when we quadruple the dimensions, the surface area is increased by a factor of 16\r<BR>\n" );
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document.write( "Hope this helps---ptaylor </SPAN>\n" );
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