document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=250791>Question 250791</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The volume, V, of a sphere is a function of its radius, r, where V = 4/3pir^3. Express the volume as a function of the diameter, d.\r<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 #184585 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=184585\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> formula in terms of radius is:\r<BR>\n" );
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document.write( "v = (4/3) * pi * r^3\r<BR>\n" );
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document.write( "radius equals diameter divided by 2:\r<BR>\n" );
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document.write( "r = d/2\r<BR>\n" );
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document.write( "replace r with (d/2) to get:\r<BR>\n" );
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document.write( "v = (4/3) * pi * (d/2)^3\r<BR>\n" );
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document.write( "(d/2)^3 is the same as (1/2)^3 * d^3 so your equation becomes:\r<BR>\n" );
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document.write( "v = (4/3) * pi * (1/2)^3 * d^3 which becomes:\r<BR>\n" );
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document.write( "v = (4/3) * pi * (1/8) * d^3\r<BR>\n" );
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document.write( "simplify to get:\r<BR>\n" );
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document.write( "v = (1/6) * pi * d^3\r<BR>\n" );
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document.write( "example:\r<BR>\n" );
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document.write( "let d = 16\r<BR>\n" );
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document.write( "that makes r = 8\r<BR>\n" );
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document.write( "v = (4/3) * pi * r^3 = (4/3) * pi * (8)^3 = (4/3) * pi * 512 = 682.67 * pi\r<BR>\n" );
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document.write( "v = (1/6) * pi * d^3 = (1/6) * pi * 16^3 = (1/6) * pi * 4096 = 682.67 * pi\r<BR>\n" );
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document.write( "both forms are equivalent, so the formula in terms of d is:\r<BR>\n" );
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document.write( "v = (1/6) * pi * d^3\r<BR>\n" );
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