document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=891065>Question 891065</A>: <I><SPAN STYLE=\"word-break: break-all;\"> There is a rectangular cuboid of dimention  x , 2x and x/3 units and a sphere of radius \" r \". The sum of their surface areas is constant.Prove that the sum of their volumes will be minimum if \" x \" is equal to three times the radius ( i.e. 3r ) of the sphere.\r<BR>\n" );
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document.write( "Please send me step by step full solution af the same.<BR>\n" );
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document.write( "regards,<BR>\n" );
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document.write( "Khoka123. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #539468 by </B><A HREF=/tutors/aboutme.mpl?userid=stanbon><B>stanbon(75887)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=stanbon><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=539468\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> There is a rectangular cuboid of dimention x , 2x and x/3 units and a sphere of radius \" r \". The sum of their surface areas is constant.Prove that the sum of their volumes will be minimum if \" x \" is equal to three times the radius ( i.e. 3r ) of the sphere.<BR>\n" );
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document.write( "Cuboid surface area = 2(x*2x + x*(x/3) + (2x)(x/3)) = 2(2x^2+(1/3)x^2+(2/3)x^2)<BR>\n" );
document.write( "= 2(3x^2) <BR>\n" );
document.write( "= 6x^2<BR>\n" );
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document.write( "Sphere surface area = 4pir^2 <BR>\n" );
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document.write( "Sum = 6x^2 + 4pir<BR>\n" );
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document.write( "Comment:: This does not lead to the predicted solution.<BR>\n" );
document.write( "Did you post the problem correctly?<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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