document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181732>Question 1181732</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A right circular cylinder with altitude equal to the diameter of its base is inscribed in a sphere. (a) compare the lateral area of the cylinder with the area of the sphere. (b) Compare the volume of the sphere with that of the cylinder. </SPAN>\n" );
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document.write( "In cross section, the diagram is a square (the cylinder) inscribed in a circle (the sphere).<br><BR>\n" );
document.write( "Draw the right triangle with vertices at (a) the center of the square/circle, (b) the center of the top of the cylinder, and (c) the point of contact of the square and the circle.<br><BR>\n" );
document.write( "That triangle is an isosceles right triangle, so the hypotenuse (the radius of the sphere) is sqrt(2) times the radius of the cylinder.<br><BR>\n" );
document.write( "So let r be the radius of the cylinder; then r*sqrt(2)is the radius of the sphere.<br><BR>\n" );
document.write( "The height of the cylinder is 2r.<br><BR>\n" );
document.write( "(a) Surface areas....<br><BR>\n" );
document.write( "Cylinder: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=2%28pi%29r%5E2%2B2%28pi%29%28r%29%28h%29+=+2%28pi%29r%5E2%2B2%28pi%29%28r%29%282r%29+=+6%28pi%29r%5E2 ALIGN=MIDDLE   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sphere: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=4%28pi%29%28r%2Asqrt%282%29%29%5E2+=+8%28pi%29r%5E2 ALIGN=MIDDLE  ALT=\"4%28pi%29%28r%2Asqrt%282%29%29%5E2+=+8%28pi%29r%5E2\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The ratio of the surface areas is 6:8 = 3:4<br><BR>\n" );
document.write( "(b) Volumes....<br><BR>\n" );
document.write( "Cylinder: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%28r%5E2%29%282r%29+=+2%28pi%29r%5E3 ALIGN=MIDDLE  ALT=\"%28pi%29%28r%5E2%29%28h%29+=+%28pi%29%28r%5E2%29%282r%29+=+2%28pi%29r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><BR>\n" );
document.write( "Sphere: <IMG STYLE=\"max-width:80%;\" SRC=/cgi-bin/plot-formula.mpl?expression=%284%2F3%29%28pi%29%28r%2Asqrt%282%29%29%5E3+=+%28%288%2F3%29sqrt%282%29%29%28pi%29r%5E3 ALIGN=MIDDLE  ALT=\"%284%2F3%29%28pi%29%28r%2Asqrt%282%29%29%5E3+=+%28%288%2F3%29sqrt%282%29%29%28pi%29r%5E3\"   DISABLED_style= \"max-width:90%; height:auto;\" ><br><BR>\n" );
document.write( "The ratio of the volumes is 2:(8/3)sqrt(2) or 1:(4/3)sqrt(2)<br><BR>\n" );
document.write( " </SPAN>\n" );
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