document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1192389>Question 1192389</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cuboid has a square base of side x cm and its height is (2x+1)cm. Find the approximate increase in its volume when x increases from 10 to 10.05 cm. Hence deduce an approximate value for the volume when<BR>\n" );
document.write( " x = 10.05 cm. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #848997 by </B><A HREF=/tutors/aboutme.mpl?userid=CPhill><B>CPhill(2189)</B></A><img src=\"/images/stars/stars-13.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=848997\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> **1. Find the Volume of the Cuboid**\r<BR>\n" );
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document.write( "* **Original Volume (V):**<BR>\n" );
document.write( "   V = Base Area × Height <BR>\n" );
document.write( "   V = x² × (2x + 1)<BR>\n" );
document.write( "   When x = 10 cm:<BR>\n" );
document.write( "   V = 10² × (2 * 10 + 1) <BR>\n" );
document.write( "   V = 100 × 21 <BR>\n" );
document.write( "   V = 2100 cubic cm\r<BR>\n" );
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document.write( "**2. Approximate Increase in Volume**\r<BR>\n" );
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document.write( "* **Use Differentials:**<BR>\n" );
document.write( "   * Volume (V) = x² * (2x + 1) = 2x³ + x²<BR>\n" );
document.write( "   * dV/dx = 6x² + 2x <BR>\n" );
document.write( "   * Approximate change in volume (dV) ≈ (dV/dx) * dx <BR>\n" );
document.write( "      where dx is the change in x (0.05 cm in this case)<BR>\n" );
document.write( "   * dV ≈ (6 * 10² + 2 * 10) * 0.05 <BR>\n" );
document.write( "   * dV ≈ (600 + 20) * 0.05 <BR>\n" );
document.write( "   * dV ≈ 31 cubic cm\r<BR>\n" );
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document.write( "**3. Approximate Volume when x = 10.05 cm**\r<BR>\n" );
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document.write( "* **Approximate New Volume:**<BR>\n" );
document.write( "   * New Volume ≈ Original Volume + Approximate Increase in Volume<BR>\n" );
document.write( "   * New Volume ≈ 2100 cubic cm + 31 cubic cm <BR>\n" );
document.write( "   * New Volume ≈ 2131 cubic cm\r<BR>\n" );
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document.write( "**Therefore:**\r<BR>\n" );
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document.write( "* **Approximate increase in volume:** 31 cubic cm<BR>\n" );
document.write( "* **Approximate volume when x = 10.05 cm:** 2131 cubic cm\r<BR>\n" );
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document.write( "This method provides an approximation of the volume change using differentials. For a more precise calculation, you could directly calculate the volume at x = 10.05 cm and compare it to the original volume.<BR>\n" );
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