document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1084033>Question 1084033</A>: <I><SPAN STYLE=\"word-break: break-all;\"> at the movies a container that holds popcorn has a square bottom base with side length of 4in and a square top with sides of 6in. The height of the container is 10 in. (front view)  Select two choices that are greater than the volume of this container <BR>\n" );
document.write( "A.a cylinder with a diameter of 5.1in and a height of 10 <BR>\n" );
document.write( "B.A square prism with lengths of the bases sides of 6.5 inches and a height of 10inches<BR>\n" );
document.write( "C.a square pyramid with a base of 36 inches and height of 10 <BR>\n" );
document.write( "D. a sphere with a radius of 4.5 inches. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #698102 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=698102\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> If option C is a square base pyramid with base sides measuring 36 inches,<BR>\n" );
document.write( "that is definitely larger.<BR>\n" );
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document.write( "If option C is a square base pyramid with base area measuring 36 square inches,<BR>\n" );
document.write( "that is smaller than all the other options.<BR>\n" );
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document.write( "The sphere (D) and the square base prism (B) are larger than the popcorn container.<BR>\n" );
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document.write( "Here is a side view of the three items:<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28675%2C300%2C-6%2C21%2C-6%2C6%2C%0D%0Acircle%280%2C0%2C4.5%29%2Carrow%280%2C0%2C0%2C4.5%29%2C%0D%0Aarrow%280%2C4.5%2C0%2C0%29%2C+locate%280.1%2C3%2C4.5in%29%2C%0D%0Aline%286%2C-5%2C12%2C-5%29%2Cline%287%2C5%2C11%2C5%29%2C%0D%0Aline%286%2C-5%2C7%2C5%29%2Cline%2812%2C-5%2C11%2C5%29%2C%0D%0Arectangle%2814%2C-5%2C20%2C5%29%2Clocate%288.5%2C-5%2C6in%29%2C%0D%0Alocate%288.5%2C5%2C4in%29%2Clocate%2816.5%2C-5%2C6in%29%2C%0D%0Alocate%2814.1%2C0.5%2C10in%29%2Clocate%28-1%2C-2%2Cshpere%29%2C%0D%0Alocate%2816%2C3%2Cprism%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "It is obvious that the popcorn container fits inside the prism.<BR>\n" );
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document.write( "The comparison with the sphere is not so obvious.<BR>\n" );
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document.write( "The shape of the popcorn container is called a frustum of a pyramid.<BR>\n" );
document.write( "That is the \"stump\" left when we cut off a pyramid parallel to its base.<BR>\n" );
document.write( "Imagine a pyramid square bottom base with side length of 6 in and a height of 30 inches.<BR>\n" );
document.write( "Its volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%281%2F3%29%28base_area%29%28height%29=%281%2F3%29%286in%29%286in%29%2830in%29=6%2A6%2A10 ALIGN=MIDDLE  ALT=\"%281%2F3%29%28base_area%29%28height%29=%281%2F3%29%286in%29%286in%29%2830in%29=6%2A6%2A10\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3 ALIGN=MIDDLE  ALT=\"in%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
document.write( "Now cut it at a height of 10 inches.<BR>\n" );
document.write( "The part above the cut is a smaller pyramid <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%2F3 ALIGN=MIDDLE  ALT=\"2%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" > scale replica of the original pyramid.<BR>\n" );
document.write( "Its volume is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282%2F3%29%5E3=8%2F27 ALIGN=MIDDLE  ALT=\"%282%2F3%29%5E3=8%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the volume of the original pyramid.<BR>\n" );
document.write( "The bottom part is your frustum.<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=drawing%28125%2C400%2C-6%2C4%2C-1%2C31%2C%0D%0Atriangle%28-3%2C0%2C3%2C0%2C0%2C30%29%2Cline%28-6%2C0%2C4%2C0%29%2C%0D%0Ared%28line%28-5.8%2C10%2C3.5%2C10%29%29%2Carrow%28-4%2C21%2C-4%2C30%29%2C%0D%0Aarrow%28-4%2C19%2C-4%2C10%29%2Clocate%28-4.8%2C20.6%2C20in%29%2C%0D%0Ared%28arrow%28-5.5%2C0%2C-5.5%2C10%29%29%2Clocate%28-5.3%2C6%2C10in%29%2C%0D%0Ared%28arrow%28-5.5%2C10%2C-5.5%2C0%29%29%2Clocate%28-1.2%2C1.3%2C6in%29%2C%0D%0Alocate%28-1.2%2C10%2C4in%29%2Cgreen%28arrow%280.2%2C30%2C-7%2C30%29%29%0D%0A%29 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" > The volume of the frustum is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=1-8%2F27=19%2F27 ALIGN=MIDDLE  ALT=\"1-8%2F27=19%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" > times the volume of the original pyramid.<BR>\n" );
document.write( "It is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%2819%2F27%29%286%2A6%2A10%29 ALIGN=MIDDLE  ALT=\"%2819%2F27%29%286%2A6%2A10%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3=19%2A6%2A6%2A10%2F27 ALIGN=MIDDLE  ALT=\"in%5E3=19%2A6%2A6%2A10%2F27\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3=19%2A4%2A10%2F3 ALIGN=MIDDLE  ALT=\"in%5E3=19%2A4%2A10%2F3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3=about253.33 ALIGN=MIDDLE  ALT=\"in%5E3=about253.33\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3 ALIGN=MIDDLE  ALT=\"in%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > .<BR>\n" );
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document.write( "The volume of the sphere is<BR>\n" );
document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%28radius%29%5E3pi=4%2A%284.5in%29%5E3%2Api%2F3=about381.7 ALIGN=MIDDLE  ALT=\"%284%2F3%29%28radius%29%5E3pi=4%2A%284.5in%29%5E3%2Api%2F3=about381.7\"   DISABLED_style= \"max-width:90%; height:auto;\" ><IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=in%5E3 ALIGN=MIDDLE  ALT=\"in%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > . </SPAN>\n" );
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