document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210363>Question 1210363</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A cone has a radius of 10cm and slant height of 26cm. find the volume of the cone </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #852075 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=852075\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to find the volume of the cone:\r<BR>\n" );
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document.write( "**1. Understand the Formulas**\r<BR>\n" );
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document.write( "To find the volume of a cone, you need its radius ($r$) and its height ($h$). The formula for the volume of a cone is:\r<BR>\n" );
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document.write( "$V = \frac{1}{3} \pi r^2 h$\r<BR>\n" );
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document.write( "You are given the radius ($r = 15 \text{ cm}$) and the slant height ($l = 20 \text{ cm}$), but you need to find the height ($h$).\r<BR>\n" );
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document.write( "**2. Find the Height (h)**\r<BR>\n" );
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document.write( "The radius, height, and slant height of a cone form a right-angled triangle, with the slant height as the hypotenuse. We can use the Pythagorean theorem:\r<BR>\n" );
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document.write( "$r^2 + h^2 = l^2$\r<BR>\n" );
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document.write( "Substitute the given values:<BR>\n" );
document.write( "$15^2 + h^2 = 20^2$<BR>\n" );
document.write( "$225 + h^2 = 400$<BR>\n" );
document.write( "$h^2 = 400 - 225$<BR>\n" );
document.write( "$h^2 = 175$<BR>\n" );
document.write( "$h = \sqrt{175}$\r<BR>\n" );
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document.write( "To simplify $\sqrt{175}$:<BR>\n" );
document.write( "$175 = 25 \times 7$<BR>\n" );
document.write( "$h = \sqrt{25 \times 7} = 5\sqrt{7} \text{ cm}$\r<BR>\n" );
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document.write( "**3. Calculate the Volume (V)**\r<BR>\n" );
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document.write( "Now that you have the height, plug the values of $r$ and $h$ into the volume formula:\r<BR>\n" );
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document.write( "$V = \frac{1}{3} \pi r^2 h$<BR>\n" );
document.write( "$V = \frac{1}{3} \pi (15)^2 (5\sqrt{7})$<BR>\n" );
document.write( "$V = \frac{1}{3} \pi (225) (5\sqrt{7})$<BR>\n" );
document.write( "$V = 75 \pi (5\sqrt{7})$<BR>\n" );
document.write( "$V = 375\sqrt{7}\pi \text{ cm}^3$\r<BR>\n" );
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document.write( "**4. Approximate the Value (Optional)**\r<BR>\n" );
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document.write( "If you need a numerical approximation, use $\pi \approx 3.14159$ and $\sqrt{7} \approx 2.64575$:\r<BR>\n" );
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document.write( "$V \approx 375 \times 2.64575 \times 3.14159$<BR>\n" );
document.write( "$V \approx 992.15625 \times 3.14159$<BR>\n" );
document.write( "$V \approx 3117.85 \text{ cm}^3$\r<BR>\n" );
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document.write( "The exact volume of the cone is $375\sqrt{7}\pi \text{ cm}^3$.<BR>\n" );
document.write( "Approximately, the volume is $3117.85 \text{ cm}^3$. </SPAN>\n" );
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