document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=262877>Question 262877</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Suppose you wish to reduce the volume of a sphere by a factor of 7.00. If it's original radius was R, what is the reduced radius in terms of R? By what factor does the sphere's surface area change? <BR>\n" );
document.write( "I have no idea how to even approach this. I'm assuming that the answers to both the questions will have 7's in them. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #193656 by </B><A HREF=/tutors/aboutme.mpl?userid=josmiceli><B>josmiceli(19441)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=josmiceli><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=josmiceli><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=193656\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The formula for the volume of a sphere is<BR>\n" );
document.write( "(1)<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%284%2F3%29%2Api%2AR%5E3 ALIGN=MIDDLE  ALT=\"V+=+%284%2F3%29%2Api%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Making the sphere seven times smaller means<BR>\n" );
document.write( "multiplying <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Let <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > = the new radius when <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1%2F7 ALIGN=MIDDLE  ALT=\"1%2F7\"   DISABLED_style= \"max-width:90%; height:auto;\" > of what it used to be<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F7%29%2AV+=+%284%2F3%29%2Api%2A%28R%5B2%5D%29%5E3 ALIGN=MIDDLE  ALT=\"%281%2F7%29%2AV+=+%284%2F3%29%2Api%2A%28R%5B2%5D%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I need to find <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Multiply both sides of (1) by <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=21 ALIGN=MIDDLE  ALT=\"21\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3V+=+28%2Api%2A%28R%5B2%5D%29%5E3 ALIGN=MIDDLE  ALT=\"3V+=+28%2Api%2A%28R%5B2%5D%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E3+=+%283V%29%2F%2828%2Api%29 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E3+=+%283V%29%2F%2828%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now I need to substitute <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (1) for <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V ALIGN=MIDDLE  ALT=\"V\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (2)<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E3+=+%283%2A%284%2F3%29%2Api%2AR%5E3%29%2F%2828%2Api%29 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E3+=+%283%2A%284%2F3%29%2Api%2AR%5E3%29%2F%2828%2Api%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E3+=+%281%2F7%29%2AR%5E3 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E3+=+%281%2F7%29%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now take the cube root of both sides<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+%281%2F7%29%5E%281%2F3%29%2AR ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+%281%2F7%29%5E%281%2F3%29%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D ALIGN=MIDDLE  ALT=\"R%5B2%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the reduced radius in terms of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R ALIGN=MIDDLE  ALT=\"R\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "The surface areas are proportional to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E2 ALIGN=MIDDLE  ALT=\"R%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E2 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Because <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A+=+4%2Api%2AR%5E2 ALIGN=MIDDLE  ALT=\"A+=+4%2Api%2AR%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "so I can rewrite (2) as<BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5B2%5D+=+%281%2F7%29%5E%281%2F3%29%2AR ALIGN=MIDDLE  ALT=\"R%5B2%5D+=+%281%2F7%29%5E%281%2F3%29%2AR\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "(2) <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%2FR+=+%281%2F7%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%2FR+=+%281%2F7%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Now square both sides<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E2%2F%28R%5E2%29+=+%28%281%2F7%29%5E%281%2F3%29%29%5E2 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E2%2F%28R%5E2%29+=+%28%281%2F7%29%5E%281%2F3%29%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28R%5B2%5D%29%5E2%2F%28R%5E2%29+=+%281%2F7%29%5E%282%2F3%29 ALIGN=MIDDLE  ALT=\"%28R%5B2%5D%29%5E2%2F%28R%5E2%29+=+%281%2F7%29%5E%282%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "This is the factor that the surface area changes by\r<BR>\n" );
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document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );