document.write( "<A HREF=/cgi-bin/jump-to-question.mpl?question=1170178>Question 1170178</A>: <I><SPAN STYLE=\"word-break: break-all;\"> 1.a) Deduce that the total surface area S of a cylinder closed at both ends with height, H and base radius R is given by: S=2πR(R+H) where π is a constant. <BR>\n" );
document.write( "b) Find the volume of S given that H =15.0m and R =5.0m (leaving your answer in terms of π)<BR>\n" );
document.write( "c) Calculate the amount of water the tank can hold leaving your answer in terms of π.<BR>\n" );
document.write( "d) Calculate the height (h) of a cuboid tank of cross-sectional area 25 metre cube which has the same capacity as the cylinder tank in (c) above.  </SPAN>\n" );
document.write( "</I><HR><TABLE width=100%><TR><TD><B><A HREF=http://www.algebra.com/>Algebra.Com's</A> Answer #851243 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=851243\">put this solution on YOUR website!</A><BR><SPAN STYLE=\"word-break: break-all;\"> Let's solve this problem step-by-step.\r<BR>\n" );
document.write( "\n" );
document.write( "**1.a) Deduce the Total Surface Area of a Closed Cylinder**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Area of the Top and Bottom Circles:** Each circle has an area of πR². Since there are two circles (top and bottom), their combined area is 2πR².<BR>\n" );
document.write( "* **Lateral Surface Area (Curved Surface):** Imagine unrolling the side of the cylinder. This forms a rectangle with height H and width equal to the circumference of the base (2πR). Therefore, the lateral surface area is 2πRH.<BR>\n" );
document.write( "* **Total Surface Area (S):** To find the total surface area, add the areas of the top, bottom, and lateral surfaces:<BR>\n" );
document.write( "    * S = 2πR² + 2πRH<BR>\n" );
document.write( "    * S = 2πR(R + H)\r<BR>\n" );
document.write( "\n" );
document.write( "**1.b) Find the Volume of the Cylinder**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Volume Formula:** The volume (V) of a cylinder is given by V = πR²H.<BR>\n" );
document.write( "* **Given Values:** H = 15.0 m and R = 5.0 m.<BR>\n" );
document.write( "* **Calculation:**<BR>\n" );
document.write( "    * V = π(5.0 m)²(15.0 m)<BR>\n" );
document.write( "    * V = π(25 m²)(15.0 m)<BR>\n" );
document.write( "    * V = 375π m³\r<BR>\n" );
document.write( "\n" );
document.write( "**1.c) Calculate the Amount of Water the Tank Can Hold**\r<BR>\n" );
document.write( "\n" );
document.write( "The amount of water the tank can hold is equal to its volume.\r<BR>\n" );
document.write( "\n" );
document.write( "* **Answer:** The tank can hold 375π m³ of water.\r<BR>\n" );
document.write( "\n" );
document.write( "**1.d) Calculate the Height of a Cuboid Tank with the Same Capacity**\r<BR>\n" );
document.write( "\n" );
document.write( "* **Cuboid Volume Formula:** The volume of a cuboid is given by V = Area of base × height.<BR>\n" );
document.write( "* **Given Information:**<BR>\n" );
document.write( "    * Volume of the cuboid = Volume of the cylinder = 375π m³<BR>\n" );
document.write( "    * Cross-sectional area (base area) of the cuboid = 25 m²<BR>\n" );
document.write( "* **Calculation:**<BR>\n" );
document.write( "    * 375π m³ = 25 m² × h<BR>\n" );
document.write( "    * h = (375π m³) / (25 m²)<BR>\n" );
document.write( "    * h = 15π m\r<BR>\n" );
document.write( "\n" );
document.write( "**Answers:**\r<BR>\n" );
document.write( "\n" );
document.write( "a)  S = 2πR(R + H)<BR>\n" );
document.write( "b)  V = 375π m³<BR>\n" );
document.write( "c)  375π m³<BR>\n" );
document.write( "d)  h = 15π m<BR>\n" );
document.write( " </SPAN>\n" );
document.write( "</TD></TR></TABLE>\n" );