document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1209538>Question 1209538</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The top of a cone of height 10cm and base radius 7cm is cut off by a plane parallel to the base. If the distance between the plane and the base is 3cm, calculate the volume of the remaining object. [Take π = 22/7]  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849362 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=849362\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the volume of the remaining object (which is a frustum):\r<BR>\n" );
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document.write( "**1. Find the radius of the top of the frustum:**\r<BR>\n" );
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document.write( "*   The original cone has a height of 10 cm and a radius of 7 cm.<BR>\n" );
document.write( "*   The top of the cone is cut off 3 cm from the base, leaving a smaller cone with a height of 10 - 3 = 7 cm.<BR>\n" );
document.write( "*   The ratio of the radius to the height in similar triangles is constant. So, the radius of the top of the frustum (r) can be found using the proportion:\r<BR>\n" );
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document.write( "r / 7 = 7 / 10<BR>\n" );
document.write( "r = (7 * 7) / 10<BR>\n" );
document.write( "r = 4.9 cm\r<BR>\n" );
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document.write( "**2. Calculate the volume of the frustum:**\r<BR>\n" );
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document.write( "The formula for the volume of a frustum is:\r<BR>\n" );
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document.write( "V = (1/3) * π * h * (R² + r² + Rr)\r<BR>\n" );
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document.write( "Where:\r<BR>\n" );
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document.write( "*   V is the volume of the frustum<BR>\n" );
document.write( "*   π is approximately 22/7<BR>\n" );
document.write( "*   h is the height of the frustum (3 cm)<BR>\n" );
document.write( "*   R is the radius of the base (7 cm)<BR>\n" );
document.write( "*   r is the radius of the top (4.9 cm)\r<BR>\n" );
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document.write( "Plugging in the values:\r<BR>\n" );
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document.write( "V = (1/3) * (22/7) * 3 * (7² + 4.9² + 7 * 4.9)<BR>\n" );
document.write( "V = (22/7) * (49 + 24.01 + 34.3)<BR>\n" );
document.write( "V = (22/7) * 107.31<BR>\n" );
document.write( "V ≈ 337.26 cm³\r<BR>\n" );
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document.write( "Therefore, the volume of the remaining object (the frustum) is approximately $\boxed{337.26}$ cm³.<BR>\n" );
document.write( " </SPAN>\n" );
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