document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1210537>Question 1210537</A>: <I><SPAN STYLE=\"word-break: break-all;\"> The curve surface area of a cylinder is 1.5 times the total surface area of a cone. If the diameter of the cylinder and cone are equal to 10cm and the vertical height of the cone is 12cm. Calculate the height of the cylinder </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #853498 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=853498\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> To find the height of the cylinder, we first need to determine the total surface area of the cone and then use the relationship provided to solve for the cylinder's height.\r<BR>\n" );
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document.write( "### 1. Find the Dimensions of the Cone\r<BR>\n" );
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document.write( "We are given the diameter of the cone is **10 cm**, so the radius () is **5 cm**. The vertical height () is **12 cm**.\r<BR>\n" );
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document.write( "To find the Total Surface Area (TSA) of a cone, we first need the **slant height ()**:\r<BR>\n" );
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document.write( "### 2. Calculate the Total Surface Area (TSA) of the Cone\r<BR>\n" );
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document.write( "The formula for the TSA of a cone is :\r<BR>\n" );
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document.write( "---\r<BR>\n" );
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document.write( "### 3. Calculate the Curved Surface Area (CSA) of the Cylinder\r<BR>\n" );
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document.write( "The problem states that the CSA of the cylinder is **1.5 times** the TSA of the cone:\r<BR>\n" );
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document.write( "### 4. Solve for the Height of the Cylinder ()\r<BR>\n" );
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document.write( "The formula for the Curved Surface Area of a cylinder is . We know the diameter is 10 cm, so the radius () is **5 cm**:\r<BR>\n" );
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document.write( "Now, divide both sides by :\r<BR>\n" );
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document.write( "**The height of the cylinder is 13.5 cm.**\r<BR>\n" );
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document.write( "Would you like me to calculate the volume of either shape to see how they compare? </SPAN>\n" );
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