document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1181778>Question 1181778</A>: <I><SPAN STYLE=\"word-break: break-all;\"> A factory's pressure tank rests on the upper base of a vertical pipe whose inside diameter is 1 and 1/2 ft. and whose length is 40 ft. The tank is a vertical cylinder surmounted by a cone, and it has a hemispherical base. If the alti tudes of the cylinder and the cone are respectively 6 ft. and 3 ft. and if all three parts of the tank have an inside diameter of 6 ft., find the volume of water in the tank and pipe when full. </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #849965 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=849965\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Here's how to calculate the total volume of water in the tank and pipe:\r<BR>\n" );
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document.write( "**1. Calculate the volume of the pipe:**\r<BR>\n" );
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document.write( "*   The pipe is a cylinder.<BR>\n" );
document.write( "*   Pipe diameter = 1.5 ft, so the radius is 1.5 ft / 2 = 0.75 ft.<BR>\n" );
document.write( "*   Pipe length (height) = 40 ft.<BR>\n" );
document.write( "*   Volume of a cylinder = π * radius² * height<BR>\n" );
document.write( "*   Pipe volume = π * (0.75 ft)² * 40 ft ≈ 70.69 ft³\r<BR>\n" );
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document.write( "**2. Calculate the volume of the cylindrical part of the tank:**\r<BR>\n" );
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document.write( "*   Tank diameter = 6 ft, so the radius is 6 ft / 2 = 3 ft.<BR>\n" );
document.write( "*   Cylinder height = 6 ft.<BR>\n" );
document.write( "*   Cylinder volume = π * (3 ft)² * 6 ft ≈ 169.65 ft³\r<BR>\n" );
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document.write( "**3. Calculate the volume of the conical part of the tank:**\r<BR>\n" );
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document.write( "*   Cone radius = 3 ft (same as the cylinder).<BR>\n" );
document.write( "*   Cone height = 3 ft.<BR>\n" );
document.write( "*   Volume of a cone = (1/3) * π * radius² * height<BR>\n" );
document.write( "*   Cone volume = (1/3) * π * (3 ft)² * 3 ft ≈ 28.27 ft³\r<BR>\n" );
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document.write( "**4. Calculate the volume of the hemispherical base:**\r<BR>\n" );
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document.write( "*   Hemisphere radius = 3 ft (same as the cylinder and cone).<BR>\n" );
document.write( "*   Volume of a hemisphere = (2/3) * π * radius³<BR>\n" );
document.write( "*   Hemisphere volume = (2/3) * π * (3 ft)³ ≈ 56.55 ft³\r<BR>\n" );
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document.write( "**5. Calculate the total volume:**\r<BR>\n" );
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document.write( "*   Total volume = Pipe volume + Cylinder volume + Cone volume + Hemisphere volume<BR>\n" );
document.write( "*   Total volume ≈ 70.69 ft³ + 169.65 ft³ + 28.27 ft³ + 56.55 ft³ ≈ 325.16 ft³\r<BR>\n" );
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document.write( "**Therefore, the volume of water in the tank and pipe when full is approximately 325.16 cubic feet.**<BR>\n" );
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