document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1086408>Question 1086408</A>: <I><SPAN STYLE=\"word-break: break-all;\"> find the volume of the pyramid formed in the octant by the plane 6x+10y+5z-30=0 and the coordinates axes  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #700603 by </B><A HREF=/tutors/aboutme.mpl?userid=KMST><B>KMST(5328)</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=700603\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> When y=z=0, you get 6x-30=0 ---> x=5.<BR>\n" );
document.write( "When x=z=0, you get 10y-30=0 ---> y=3.<BR>\n" );
document.write( "When x=y=0, you get 5z-30=0 ---> z=6.<BR>\n" );
document.write( "That plane intersects the coordinate axes at points<BR>\n" );
document.write( "(5,0,0) , (0,3,0) , and (0,0,6) .<BR>\n" );
document.write( "You could say that the base is the triangle on the x-z plane with vertices (0,0,0) , (5,0,0) , and (0,0,6) ,<BR>\n" );
document.write( "and that the altitude is the segment on the y-axis between<BR>\n" );
document.write( "(0,0,0) , and (0,3,0) .<BR>\n" );
document.write( "So, the area of the base of that pyramid is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6%2A5%2F2=15 ALIGN=MIDDLE  ALT=\"6%2A5%2F2=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > ,<BR>\n" );
document.write( "and the height is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=3 ALIGN=MIDDLE  ALT=\"3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "The volume would be<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%2A15%2A3=15 ALIGN=MIDDLE  ALT=\"%281%2F3%29%2A15%2A3=15\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( " <BR>\n" );
document.write( "DRAWING ADDED UPON REQUEST:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28400%2C350%2C-4%2C4%2C-2%2C5%2C%0D%0Alocate%28-3.8%2C-1.8%2Cx%29%2Clocate%283.6%2C-1.65%2Cy%29%2C%0D%0Alocate%280%2C4.8%2Cz%29%2C%0D%0Aline%280%2C0%2C-3.6%2C-1.8%29%2Carrow%28-0.8%2C-0.4%2C-3.6%2C-1.8%29%2C%0D%0Aline%280%2C0%2C3.5%2C-1.75%29%2Carrow%281%2C-0.5%2C3.5%2C-1.75%29%2C%0D%0Aline%280%2C0%2C0%2C4.4%29%2Carrow%280%2C2%2C0%2C4.4%29%2C%0D%0Agreen%28arrow%280.5%2C-0.25%2C-5%2C-3%29%29%2C%0D%0Agreen%28arrow%281%2C-0.5%2C-5%2C-3.5%29%29%2C%0D%0Agreen%28arrow%281.5%2C-0.75%2C-5%2C-4%29%29%2C%0D%0Agreen%28arrow%282%2C-1%2C-5%2C-4.5%29%29%2C%0D%0Agreen%28arrow%282.5%2C-1.25%2C-5%2C-5%29%29%2C%0D%0Agreen%28arrow%283%2C-1.5%2C-5%2C-5.5%29%29%2C%0D%0Agreen%28arrow%28-0.5%2C-0.25%2C6%2C-3.5%29%29%2C%0D%0Agreen%28arrow%28-1%2C-0.5%2C6%2C-4%29%29%2C%0D%0Agreen%28arrow%28-1.5%2C-0.75%2C6%2C-4.5%29%29%2C%0D%0Agreen%28arrow%28-2%2C-1%2C6%2C-5%29%29%2C%0D%0Agreen%28arrow%28-2.5%2C-1.25%2C6%2C-5.5%29%29%2C%0D%0Agreen%28arrow%28-3%2C-1.+5%2C6%2C-6%29%29%2C%0D%0Aline%28-0.05%2C0.5%2C0.05%2C0.5%29%2C%0D%0Aline%28-0.05%2C1%2C0.05%2C1%29%2C%0D%0Aline%28-0.05%2C1.5%2C0.05%2C1.5%29%2C%0D%0Aline%28-0.05%2C2%2C0.05%2C2%29%2C%0D%0Aline%28-0.05%2C2.5%2C0.05%2C2.5%29%2C%0D%0Aline%28-0.05%2C3%2C0.05%2C3%29%2C%0D%0Aline%28-0.05%2C3.5%2C0.05%2C3.5%29%2C%0D%0Aline%281.5%2C-0.75%2C-2.5%2C-1.25%29%2C%0D%0Aline%281.5%2C-0.75%2C0%2C3%29%2C%0D%0Aline%280%2C3%2C-2.5%2C-1.25%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );