document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1203337>Question 1203337</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A frustum of a sphere of radius 13 cm is formed by two parallel planes on opposite sides of the center, each at distance of 5 cm from the center. Determine the volume of the frustum (a) by using the prismoidal rule, and (b) by using the formula for the volume of a frustum of a sphere </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #838822 by </B><A HREF=/tutors/aboutme.mpl?userid=Alan3354><B>Alan3354(69443)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=Alan3354><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=Alan3354><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=838822\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> A frustum of a sphere of radius 13 cm is formed by two parallel planes on opposite sides of the center, each at distance of 5 cm from the center. Determine the volume of the frustum (a) by using the prismoidal rule, and (b) by using the formula for the volume of a frustum of a sphere<BR>\n" );
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document.write( "Find the volumes of the 2 segments NOT in the frustum:<BR>\n" );
document.write( "For each:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2Ah%5E2%2A%283r-h%29%2F3 ALIGN=MIDDLE  ALT=\"V+=+pi%2Ah%5E2%2A%283r-h%29%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > where r = 13 and and h = 6.5-5 = 1.5<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+pi%2A64%2839-1.5%29%2F3+=+800pi ALIGN=MIDDLE  ALT=\"V+=+pi%2A64%2839-1.5%29%2F3+=+800pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > for each<BR>\n" );
document.write( "---> 1600pi<BR>\n" );
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document.write( "Subtract that from the volume of the shpere:<BR>\n" );
document.write( "---> <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%2Api%2A13%5E3%2F3+-+4800pi%2F3+=+2396%2Api ALIGN=MIDDLE  ALT=\"4%2Api%2A13%5E3%2F3+-+4800pi%2F3+=+2396%2Api\"   DISABLED_style= \"max-width:90%; height:auto;\" > cc<BR>\n" );
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document.write( "h = the distance from the surface of the sphere to the plane on the diameter.<BR>\n" );
document.write( "PS  This is an equation used in the calculation of the volume of a liquid in a spherical tank where h would be the depth of the liquid.<BR>\n" );
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document.write( "I mistakenly used 13 as the diameter when it's the radius.<BR>\n" );
document.write( "The method is good, tho.<BR>\n" );
document.write( "The student can redo it using 13 instead of 6.5 </SPAN>\n" );
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