document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=149517>Question 149517</A>: <I><SPAN STYLE=\"word-break: break-all;\"> Find the volume of material that is needed to form a spherical shell whose outer radius is 6.0 inches and whose thickness is 0.01 inches. Use your answer to estimate the surface area of the 6-inch sphere.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #109697 by </B><A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><B>jim_thompson5910(35256)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=jim_thompson5910><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/images/nopicture.jpg><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=109697\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> First let's find the volume of the outer sphere. Note: I'm going to call this volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%284%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"V=%284%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the volume of a sphere formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D=%284%2F3%29pi%2A%286%29%5E3 ALIGN=MIDDLE  ALT=\"V%5Bo%5D=%284%2F3%29pi%2A%286%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=6 ALIGN=MIDDLE  ALT=\"r=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D=%284%2F3%29pi%2A%28216%29 ALIGN=MIDDLE  ALT=\"V%5Bo%5D=%284%2F3%29pi%2A%28216%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube 6 to get 216\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D=904.77868 ALIGN=MIDDLE  ALT=\"V%5Bo%5D=904.77868\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "So the volume of the outer sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D=904.77868 ALIGN=MIDDLE  ALT=\"V%5Bo%5D=904.77868\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "Now let's find the volume of the inner sphere. Since the shell is 0.01 inches thick, this means that the inner radius is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=6-0.01=5.99 ALIGN=MIDDLE  ALT=\"6-0.01=5.99\"   DISABLED_style= \"max-width:90%; height:auto;\" > inches.\r<BR>\n" );
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document.write( " Note: I'm going to call this volume <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D ALIGN=MIDDLE  ALT=\"V%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V=%284%2F3%29pi%2Ar%5E3 ALIGN=MIDDLE  ALT=\"V=%284%2F3%29pi%2Ar%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the volume of a sphere formula.\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D=%284%2F3%29pi%2A%285.99%29%5E3 ALIGN=MIDDLE  ALT=\"V%5Bi%5D=%284%2F3%29pi%2A%285.99%29%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=5.99 ALIGN=MIDDLE  ALT=\"r=5.99\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D=%284%2F3%29pi%2A%28214.92%29 ALIGN=MIDDLE  ALT=\"V%5Bi%5D=%284%2F3%29pi%2A%28214.92%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Cube 5.99 to get 214.92\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D=900.26232 ALIGN=MIDDLE  ALT=\"V%5Bi%5D=900.26232\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply.\r<BR>\n" );
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document.write( "So the volume of the inner sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D=900.26232 ALIGN=MIDDLE  ALT=\"V%5Bi%5D=900.26232\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So to find the volume of the shell, simply subtract the volume of the inner sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bi%5D ALIGN=MIDDLE  ALT=\"V%5Bi%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > from the volume of the outer sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D ALIGN=MIDDLE  ALT=\"V%5Bo%5D\"   DISABLED_style= \"max-width:90%; height:auto;\" > like this\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V%5Bo%5D-V%5Bi%5D=904.77868-900.26232=4.51636 ALIGN=MIDDLE  ALT=\"V%5Bo%5D-V%5Bi%5D=904.77868-900.26232=4.51636\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "So the volume of the shell is about 4.52 cubic inches\r<BR>\n" );
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document.write( "To find the surface area of the outer sphere, simply use this formula <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=4pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4pi%2Ar%5E2 ALIGN=MIDDLE  ALT=\"A=4pi%2Ar%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Start with the surface area formula\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4pi%2A%286%29%5E2 ALIGN=MIDDLE  ALT=\"A=4pi%2A%286%29%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" > Plug in <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=r=6 ALIGN=MIDDLE  ALT=\"r=6\"   DISABLED_style= \"max-width:90%; height:auto;\" >\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=4pi%2A%2836%29 ALIGN=MIDDLE  ALT=\"A=4pi%2A%2836%29\"   DISABLED_style= \"max-width:90%; height:auto;\" > Square 6 to get 36\r<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=144pi ALIGN=MIDDLE  ALT=\"A=144pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > Multiply\r<BR>\n" );
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document.write( "So the surface area of the outer sphere is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=A=144pi ALIGN=MIDDLE  ALT=\"A=144pi\"   DISABLED_style= \"max-width:90%; height:auto;\" > which is approximately 452.39 square inches.\r<BR>\n" );
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