document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1205074>Question 1205074</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A spherical piece of steel is 1/8\" in diameter.\r<BR>\n" );
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document.write( "1).  Determine volume.\r<BR>\n" );
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document.write( "2).  Determine how many could be produced from 1 cu. in. of the material.\r<BR>\n" );
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document.write( "Check my calculations, please.\r<BR>\n" );
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document.write( "Sphere volume:  4/3 * pi * r^3\r<BR>\n" );
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document.write( "1.333 * 3.1416 * .0625^3\r<BR>\n" );
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document.write( "= .01021 cu. in.  1).\r<BR>\n" );
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document.write( "1 / .01021 = 97.84 = 98 2).\r<BR>\n" );
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document.write( "Part 1\r<BR>\n" );
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document.write( "Diameter = 1/8<BR>\n" );
document.write( "Radius = 1/16 which is half the diameter\r<BR>\n" );
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document.write( "Volume = (4/3)*pi*(radius)^3<BR>\n" );
document.write( "Volume = (4/3)*pi*(1/16)^3<BR>\n" );
document.write( "Volume = 0.0010226538586<BR>\n" );
document.write( "I kept the fraction 4/3 and I let the calculator handle the decimal digits of pi, so I could get the most accuracy possible.<BR>\n" );
document.write( "Round that decimal value however needed.\r<BR>\n" );
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document.write( "It appears you forgot a zero in your result of .01021\r<BR>\n" );
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document.write( "Part 2\r<BR>\n" );
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document.write( "n = number of spheres<BR>\n" );
document.write( "0.0010226538586 = volume of 1 sphere<BR>\n" );
document.write( "0.0010226538586n = volume of n spheres = amount of material<BR>\n" );
document.write( "0.0010226538586n = 1<BR>\n" );
document.write( "n = 1/0.0010226538586<BR>\n" );
document.write( "n = 977.847970347451<BR>\n" );
document.write( "n = 977\r<BR>\n" );
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document.write( "We can make about 977 spheres.\r<BR>\n" );
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document.write( "Your answer is off by a factor of 10 because you forgot a zero in your previous result.<BR>\n" );
document.write( "Your previous result should be smaller by a factor of 10, making the second result larger by a factor of 10 (to counter-balance).\r<BR>\n" );
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document.write( "In cases like this, always <font color=red>round down</font> to the nearest whole number. It doesn't matter that n = 977.84797 is closer to 978 compared to 977.<BR>\n" );
document.write( "We do not have enough material to make the 978<sup>th</sup> sphere.\r<BR>\n" );
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document.write( "If you made 977 spheres, then you use up <BR>\n" );
document.write( "0.0010226538586*977 = 0.9991328198522 cubic inches of material\r<BR>\n" );
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document.write( "But if you made 978 spheres, then you use up<BR>\n" );
document.write( "0.0010226538586*978 = 1.0001554737108 cubic inches<BR>\n" );
document.write( "Which is over the target of \"1 cubic inch\".<BR>\n" );
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