document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1064469>Question 1064469</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A) The formula for the volume of a sphere of radius r is V(r) = 4/3&#960;r^3. Solve this equation for r. Write two versions, one in radical form and one in exponential form. \r<BR>\n" );
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document.write( "B) Determine the radius of a sphere with a volume of 256&#960;/3 m^3  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #679518 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=679518\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> v = 4/3 * pi * r^3\r<BR>\n" );
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document.write( "solve for r in radical form.\r<BR>\n" );
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document.write( "start with v = 4/3 * pi * r^3<BR>\n" );
document.write( "divide both sides of the equation by (4/3 * pi) to get:<BR>\n" );
document.write( "v/(4/3 * pi) = r^3<BR>\n" );
document.write( "this can be simplified to (3v/4 * pi) = r^3<BR>\n" );
document.write( "take the third root of each side of the equation to get:\r<BR>\n" );
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document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=root%283%2C3v%2F%284%2Api%29%29%29 ALIGN=MIDDLE  ALT=\"root%283%2C3v%2F%284%2Api%29%29%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "solve for r in exponent form.\r<BR>\n" );
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document.write( "same process except the result is shown as:\r<BR>\n" );
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document.write( "r = <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%283v%2F%284%2Api%29%29%5E%281%2F3%29 ALIGN=MIDDLE  ALT=\"%283v%2F%284%2Api%29%29%5E%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "last question:\r<BR>\n" );
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document.write( "v = 256&#960;/3\r<BR>\n" );
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document.write( "solve for r.\r<BR>\n" );
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document.write( "r should be equal to <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28%28%283+%2A+256+%2A+pi+%2F+3%29%29+%2F+%284+%2A+pi%29%29+%5E+%281%2F3%29 ALIGN=MIDDLE  ALT=\"%28%28%283+%2A+256+%2A+pi+%2F+3%29%29+%2F+%284+%2A+pi%29%29+%5E+%281%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "that would make r equal to 4.\r<BR>\n" );
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document.write( "to see if this is correct, go back to the volume formula of v = 4/3 * pi * r^3\r<BR>\n" );
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document.write( "that formula becomes v = 4/3 * pi * 4^3 which becomes v = 4/3 * pi * 64 which becomes v = 256 * pi / 3.\r<BR>\n" );
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document.write( "this is the same as v = 256pi/3 which is where we started from, so the solution looks good.\r<BR>\n" );
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document.write( "i used pi instead of the symbol for pi that you showed.<BR>\n" );
document.write( "pi means the same thing as &#960;\r<BR>\n" );
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document.write( "it's not as formal, but it's a lot quicker to do it that way.\r<BR>\n" );
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document.write( "works fine unless you're required to use the proper mathematical symbol.\r<BR>\n" );
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