document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1198557>Question 1198557</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The frustum of a cone of revolution is 25 cm high, and the radii of its bases are 8 cm and 2 cm, respectively. Find the height, in cm, of an equivalent right circular cylinder whose base is equal in area to the section of the frustum made by a plane parallel to its base and equidistant from the bases. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848332 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=848332\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Certainly, let's find the height of the equivalent cylinder.\r<BR>\n" );
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document.write( "**1. Find the Radius of the Midsection**\r<BR>\n" );
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document.write( "* Since the cutting plane is equidistant from the bases, it divides the frustum's height equally.<BR>\n" );
document.write( "* Height of each portion = 25 cm / 2 = 12.5 cm\r<BR>\n" );
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document.write( "* We can use similar triangles to find the radius (r) of the midsection:\r<BR>\n" );
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document.write( "   * (r - 2) / 12.5 = (8 - 2) / 25 <BR>\n" );
document.write( "   * (r - 2) / 12.5 = 6 / 25<BR>\n" );
document.write( "   * r - 2 = (6 * 12.5) / 25<BR>\n" );
document.write( "   * r - 2 = 3<BR>\n" );
document.write( "   * r = 5 cm\r<BR>\n" );
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document.write( "**2. Find the Area of the Midsection**\r<BR>\n" );
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document.write( "* Area of the midsection (A) = π * r² <BR>\n" );
document.write( "* A = π * (5 cm)² <BR>\n" );
document.write( "* A = 25π cm²\r<BR>\n" );
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document.write( "**3. Find the Volume of the Frustum**\r<BR>\n" );
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document.write( "* Volume of Frustum (V) = (1/3) * π * h * (R² + r² + Rr) <BR>\n" );
document.write( "    * Where:<BR>\n" );
document.write( "        * h = height of frustum (25 cm)<BR>\n" );
document.write( "        * R = radius of larger base (8 cm)<BR>\n" );
document.write( "        * r = radius of smaller base (2 cm)\r<BR>\n" );
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document.write( "* V = (1/3) * π * 25 * (8² + 2² + 8 * 2)<BR>\n" );
document.write( "* V = (1/3) * π * 25 * (64 + 4 + 16)<BR>\n" );
document.write( "* V = (1/3) * π * 25 * 84<BR>\n" );
document.write( "* V = 700π cm³\r<BR>\n" );
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document.write( "**4. Find the Volume of the Equivalent Cylinder**\r<BR>\n" );
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document.write( "* Volume of Cylinder (V) = Area of Base * Height <BR>\n" );
document.write( "* 700π cm³ = 25π cm² * Height <BR>\n" );
document.write( "* Height = 700π cm³ / 25π cm² <BR>\n" );
document.write( "* Height = 28 cm\r<BR>\n" );
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document.write( "**Therefore, the height of the equivalent right circular cylinder is 28 cm.**<BR>\n" );
document.write( " </SPAN>\n" );
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