document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1081843>Question 1081843</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Hi, I really need help with this question: \r<BR>\n" );
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document.write( "A cone has the same base radius as the radius of a sphere. If the volumes of the cone and the sphere are equal, by what factor is the height of the cone larger than its base radius?\r<BR>\n" );
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document.write( "Thank you!  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #695892 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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=695892\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of the sphere is<BR>\n" );
document.write( "Vs = (4/3)*pi*r^3<BR>\n" );
document.write( "where r is the radius\r<BR>\n" );
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document.write( "The volume of the cone is<BR>\n" );
document.write( "Vc = (1/3)*pi*r^2*h<BR>\n" );
document.write( "where r is the radius of the base and h is the height\r<BR>\n" );
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document.write( "Note: Since the problem states that \"A cone has the same base radius as the radius of a sphere\", we can use the variable r twice.\r<BR>\n" );
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document.write( "Since we're told that \"the volumes of the cone and the sphere are equal\", we can say<BR>\n" );
document.write( "Vc = Vs<BR>\n" );
document.write( "(1/3)*pi*r^2*h = (4/3)*pi*r^3<BR>\n" );
document.write( "3*(1/3)*pi*r^2*h = 3*(4/3)*pi*r^3  <font color=blue>multiply both sides by 3</font><BR>\n" );
document.write( "pi*r^2*h = 4*pi*r^3 <BR>\n" );
document.write( "(pi*r^2*h)/pi = (4*pi*r^3)/pi  <font color=blue>divide both sides by pi</font><BR>\n" );
document.write( "r^2*h = 4*r^3<BR>\n" );
document.write( "(r^2*h)/(r^2) = (4*r^3)/(r^2)  <font color=blue>divide both sides by r^2</font><BR>\n" );
document.write( "h = 4*r\r<BR>\n" );
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document.write( "After isolating h, we get h = 4*r indicating that <font color=red>the height is 4 times the base radius</font>.  </SPAN>\n" );
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