document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210593>Question 1210593</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Help me for ths question please.\r<BR>\n" );
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document.write( "a. The region bounded by the circle x2+y2=a2 is the base of a solid. Cross sections taken perpendicular to the base and parallel to the y-axis are equilateral triangles.\r<BR>\n" );
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document.write( "Find the volume of the solid.\r<BR>\n" );
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document.write( "b.  A cylindrical hole of constant radius r and height h is bored through the centre of a sphere with radius R.\r<BR>\n" );
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document.write( "Find the volume of the solid in terms of h.\r<BR>\n" );
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document.write( "c.  The region bounded by the curve y=−x2+4x−3 and the x-axis is rotated about the line x=3 to form a solid.\r<BR>\n" );
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document.write( "Find the volume of the solid. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #854154 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5344)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=KMST><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=KMST><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=854154\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Reading phrase by phrase and understanding:<BR>\n" );
document.write( "\"The region bounded by the circle <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x%5E2%2By%5E2=a%5E2 ALIGN=MIDDLE  ALT=\"x%5E2%2By%5E2=a%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > is the base of a solid.\"<BR>\n" );
document.write( "The base of the solid is a circle on the x-y plane, with center at the origin, radius <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a ALIGN=MIDDLE  ALT=\"a\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and diameter <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "So, far we know that the area of that base is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Aa%5E2 ALIGN=MIDDLE  ALT=\"pi%2Aa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "\"Cross sections taken perpendicular to the base and parallel to the y-axis are equilateral triangles.\"<BR>\n" );
document.write( "The y-axis is the line <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=0 ALIGN=MIDDLE  ALT=\"x=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > , and the cross sections mentioned are obtained cutting through the solid through planes <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=b ALIGN=MIDDLE  ALT=\"x=b\"   DISABLED_style= \"max-width:90%; height:auto;\" > with values of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=b ALIGN=MIDDLE  ALT=\"b\"   DISABLED_style= \"max-width:90%; height:auto;\" > in (-a,a) .<BR>\n" );
document.write( "Those cross sections have a base on the x-y plane, and they are equilateral triangles.<BR>\n" );
document.write( "The largest such equilateral triangle has a base of length <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2a ALIGN=MIDDLE  ALT=\"2a\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "extending between the points (0,-a), and (0,a), and a height of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28sqrt%283%29%2F2%29%2A%282a%29=a%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"%28sqrt%283%29%2F2%29%2A%282a%29=a%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "with a vertex at the point with coordinates <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=x=y=0 ALIGN=MIDDLE  ALT=\"x=y=0\"   DISABLED_style= \"max-width:90%; height:auto;\" > and <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=z=a%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"z=a%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > , which is the apex of the solid.<BR>\n" );
document.write( "Intuitively, we know the solid is a cone.<BR>\n" );
document.write( "Hopefully we do not need to prove that through a lot of boring algebra and geometry work.<BR>\n" );
document.write( "The volume of that cone with base area <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=pi%2Aa%5E2 ALIGN=MIDDLE  ALT=\"pi%2Aa%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > and height <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=a%2Asqrt%283%29 ALIGN=MIDDLE  ALT=\"a%2Asqrt%283%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28pi%2Aa%5E2%29%28a%2Asqrt%283%29%29=highlight%28a%5E3%2Api%2Asqrt%283%29%2F3%29 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28pi%2Aa%5E2%29%28a%2Asqrt%283%29%29=highlight%28a%5E3%2Api%2Asqrt%283%29%2F3%29\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( " </SPAN>\n" );
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