document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1037678>Question 1037678</A>: <I><SPAN STYLE=\"word-break: break-all;\"> In the process of making a sphere out of marble, the first step is to cut the rough piece of marble into a cube.  After this, rough cuts are made to get rid of as many corners as possible.  Then, the sculptor grinds away any sharp edges.  The result is a roundish piece of rock that is put into another grinding machine that has two cupped grinders rotating in opposite directions.   \r<BR>\n" );
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document.write( "a. What volume of rock was in the cube if the original piece of rock was cut into a cube with side lengths of 60 mm?  Round to the nearest cubic millimetre.<BR>\n" );
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document.write( "b. What is the maximum diameter of the sphere that could be made from the cube?<BR>\n" );
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document.write( "c. If the sphere has the maximum diameter, what is the volume of rock in the sphere at the end of the process?  Round to the nearest cubic millimetre.  <BR>\n" );
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document.write( "d. How much rock was cut or ground away?<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 #652338 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=652338\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> In the process of making a sphere out of marble, the first step is to cut the rough piece of marble into a cube. After this, rough cuts are made to get rid of as many corners as possible. Then, the sculptor grinds away any sharp edges. The result is a roundish piece of rock that is put into another grinding machine that has two cupped grinders rotating in opposite directions. <BR>\n" );
document.write( "a. What volume of rock was in the cube if the original piece of rock was cut into a cube with side lengths of 60 mm? Round to the nearest cubic millimetre.<BR>\n" );
document.write( "Ans: 60^3 = 216000 mm^3<BR>\n" );
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document.write( "b. What is the maximum diameter of the sphere that could be made from the cube?<BR>\n" );
document.write( "Ans: 60mm<BR>\n" );
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document.write( "c. If the sphere has the maximum diameter, what is the volume of rock in the sphere at the end of the process? Round to the nearest cubic millimetre.<BR>\n" );
document.write( "V = (4/3)pi*r^3<BR>\n" );
document.write( "V = (4/3)pi*30^3 = 113,097 mm^3<BR>\n" );
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document.write( "d. How much rock was cut or ground away?<BR>\n" );
document.write( "216000- 113.097 = 102,903 mm^3<BR>\n" );
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document.write( "Cheers,<BR>\n" );
document.write( "Stan H.<BR>\n" );
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