document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181724>Question 1181724</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 17.	Find the volume of the largest right circular cylinder of altitude 8 in. that can be cut from a sphere of diameter 12 in. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849976 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(1959)</B></A><img src=\"/images/stars/stars-12.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=CPhill><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=CPhill><BR>You can <A HREF=\"/cgi-bin/embed-solution.mpl?show=1&solution=849976\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the volume of the largest cylinder:\r<BR>\n" );
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document.write( "**1. Visualize the Setup:** Imagine a sphere with a cylinder inside it. The cylinder's height is fixed at 8 inches, and we want to find the largest possible radius for the cylinder.\r<BR>\n" );
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document.write( "**2. Key Dimensions:**\r<BR>\n" );
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document.write( "*   Sphere diameter = 12 inches, so sphere radius (R) = 6 inches.<BR>\n" );
document.write( "*   Cylinder height (h) = 8 inches.<BR>\n" );
document.write( "*   Let 'r' be the radius of the cylinder.\r<BR>\n" );
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document.write( "**3. Cross-Section:**  A cross-section through the center of the sphere and cylinder reveals a circle (the sphere) with a rectangle (the cylinder) inside.  The diagonal of this rectangle is the diameter of the sphere (12 inches).\r<BR>\n" );
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document.write( "**4. Pythagorean Theorem:** We can use the Pythagorean theorem to relate the sphere's radius (R), the cylinder's radius (r), and *half* of the cylinder's height (h/2):\r<BR>\n" );
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document.write( "R² = r² + (h/2)²\r<BR>\n" );
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document.write( "**5. Solve for the Cylinder's Radius (r):**\r<BR>\n" );
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document.write( "6² = r² + (8/2)²<BR>\n" );
document.write( "36 = r² + 16<BR>\n" );
document.write( "r² = 20<BR>\n" );
document.write( "r = √20 = 2√5 inches\r<BR>\n" );
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document.write( "**6. Volume of the Cylinder:**\r<BR>\n" );
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document.write( "Volume of a cylinder = πr²h<BR>\n" );
document.write( "V = π(2√5)² * 8<BR>\n" );
document.write( "V = π * 20 * 8<BR>\n" );
document.write( "V = 160π cubic inches\r<BR>\n" );
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document.write( "**Therefore, the volume of the largest right circular cylinder is 160π cubic inches, or approximately 502.65 cubic inches.**<BR>\n" );
document.write( " </SPAN>\n" );
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