document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198562>Question 1198562</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The bases of a frustum of a right circular cone are circles whose diameters are respectively 18 and 14 inches. With a slant height of 25 inches, the volume may be expressed as V = Χπ √γ in^3 where Χ and γ are integers. Find the smallest sum of  Χ and γ. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848330 by </B><A HREF=/tutors/aboutme.mpl?userid=onyulee><B>onyulee(41)</B></A><img src=\"/images/stars/stars-07.gif\" alt=\"\" >&nbsp;<A HREF=/tutors/aboutme.mpl?userid=onyulee><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=848330\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Radii**\r<BR>\n" );
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document.write( "* Radius of the larger base (R) = 18 inches / 2 = 9 inches<BR>\n" );
document.write( "* Radius of the smaller base (r) = 14 inches / 2 = 7 inches\r<BR>\n" );
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document.write( "**2. Find the Height of the Frustum**\r<BR>\n" );
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document.write( "* Let 'h' be the height of the frustum.<BR>\n" );
document.write( "* We have a right triangle formed by:<BR>\n" );
document.write( "    * Slant height (l) = 25 inches<BR>\n" );
document.write( "    * Height (h)<BR>\n" );
document.write( "    * Difference in radii (R - r) = 9 - 7 = 2 inches\r<BR>\n" );
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document.write( "* Using the Pythagorean Theorem:<BR>\n" );
document.write( "    * h² = l² - (R - r)²<BR>\n" );
document.write( "    * h² = 25² - 2²<BR>\n" );
document.write( "    * h² = 625 - 4<BR>\n" );
document.write( "    * h² = 621<BR>\n" );
document.write( "    * h = √621 inches\r<BR>\n" );
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document.write( "**3. Calculate the Volume of the Frustum**\r<BR>\n" );
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document.write( "* Volume (V) = (1/3) * π * h * (R² + Rr + r²) <BR>\n" );
document.write( "* V = (1/3) * π * √621 * (9² + 9*7 + 7²)<BR>\n" );
document.write( "* V = (1/3) * π * √621 * (81 + 63 + 49)<BR>\n" );
document.write( "* V = (1/3) * π * √621 * 193\r<BR>\n" );
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document.write( "**4. Express the Volume in the Given Form**\r<BR>\n" );
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document.write( "* V = (193/3) * π * √621 <BR>\n" );
document.write( "* V = Χπ√γ \r<BR>\n" );
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document.write( "* **Χ = 193/3** <BR>\n" );
document.write( "* **γ = 621**\r<BR>\n" );
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document.write( "**5. Find the Smallest Sum of Χ and γ**\r<BR>\n" );
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document.write( "* Sum = Χ + γ = (193/3) + 621 <BR>\n" );
document.write( "* Sum = 193/3 + 1863/3 <BR>\n" );
document.write( "* Sum = 2056/3 \r<BR>\n" );
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document.write( "**Therefore, the smallest sum of Χ and γ is 2056/3.**<BR>\n" );
document.write( " </SPAN>\n" );
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