document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=117579>Question 117579</A>: <I><SPAN STYLE=\"word-break: break-all;\"> calculate and compare the volume of three pairs of spheres with the following radii.\r<BR>\n" );
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document.write( "pair 1 (r =1', r=2') pair 2 (r = 3', r', = 6') pair 3 (r=4',r=8')<BR>\n" );
document.write( "What happens to the volume of a sphere if its radius is doubled?  Why?\r<BR>\n" );
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document.write( "thank you </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #85567 by </B><A HREF=/tutors/aboutme.mpl?userid=bucky><B>bucky(2189)</B></A><img src=\"/images/stars/stars-13.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=bucky><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=85567\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> The volume of a sphere (V) can be calculated using the equation:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+%284%2F3%29%2A%28pi%29%2AR%5E3 ALIGN=MIDDLE  ALT=\"V+=+%284%2F3%29%2A%28pi%29%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "in which R represents the radius of the sphere. If you multiply out the constants:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%2A%28pi%29 ALIGN=MIDDLE  ALT=\"%284%2F3%29%2A%28pi%29\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "you get a product 4.18879025 and substituting this product into the volume equation simplifies<BR>\n" );
document.write( "it to:<BR>\n" );
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document.write( "<IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=V+=+4.18879025%2AR%5E3 ALIGN=MIDDLE  ALT=\"V+=+4.18879025%2AR%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
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document.write( "Using this form of the equation, all you have to do for this problem is enter the constant 4.18879025<BR>\n" );
document.write( "into your calculator's memory. Then for each of the given spheres, cube its radius and <BR>\n" );
document.write( "multiply that by the constant which you can recall from memory.<BR>\n" );
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document.write( "For example. The first pair ... one sphere has a radius of 1 ft. Cube that to get 1 cu ft<BR>\n" );
document.write( "and multiply that by 4.18879025 to get an answer of 4.18879025 cu ft.<BR>\n" );
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document.write( "The first pair ... second sphere has a radius of 2 ft. Cube that and you get 8 cu ft. Then <BR>\n" );
document.write( "multiply that by 4.18879025 and you get the volume to be 33.51032164 cu ft.<BR>\n" );
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document.write( "It may be apparent to you now that when you doubled the radius the volume went up 8 times.<BR>\n" );
document.write( "That is because the cube of R is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=R%5E3 ALIGN=MIDDLE  ALT=\"R%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" > and the cube of 2R is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%282R%29%5E3+=+2%5E3+%2AR%5E3+=+8R%5E3 ALIGN=MIDDLE  ALT=\"%282R%29%5E3+=+2%5E3+%2AR%5E3+=+8R%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" >. <BR>\n" );
document.write( "The ratio of these two is <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%288R%5E3%29%2FR%5E3+=+8 ALIGN=MIDDLE  ALT=\"%288R%5E3%29%2FR%5E3+=+8\"   DISABLED_style= \"max-width:90%; height:auto;\" >.<BR>\n" );
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document.write( "You can now apply this same technique to the remaining 2 pairs of spheres. When you do, you<BR>\n" );
document.write( "should get the following answers:<BR>\n" );
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document.write( "Pair 2. The sphere with the radius of 3 ft has a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.18879025%2A3%5E3+=+113.0973355+ ALIGN=MIDDLE  ALT=\"4.18879025%2A3%5E3+=+113.0973355+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu ft<BR>\n" );
document.write( "and the sphere with the radius of 6 ft has a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.18879025%2A6%5E3+=+904.7786842+ ALIGN=MIDDLE  ALT=\"4.18879025%2A6%5E3+=+904.7786842+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu ft<BR>\n" );
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document.write( "Pair 3. The sphere with the radius of 4 ft has a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.18879025%2A4%5E3+=+268.0825731+ ALIGN=MIDDLE  ALT=\"4.18879025%2A4%5E3+=+268.0825731+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu ft<BR>\n" );
document.write( "and the sphere with the radius of 8 ft has a volume of <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4.18879025%2A8%5E3+=+2144.660585+ ALIGN=MIDDLE  ALT=\"4.18879025%2A8%5E3+=+2144.660585+\"   DISABLED_style= \"max-width:90%; height:auto;\" > cu ft<BR>\n" );
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document.write( "In each pair, if you take divide the answer for the volume of the first sphere into the answer<BR>\n" );
document.write( "for the volume of the second sphere you should get an answer of 8.<BR>\n" );
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document.write( "Hope this helps you to understand the problem and how you can work it.<BR>\n" );
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