Lesson OVERVIEW of LESSONS on Surface Area of CYLINDERS

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<H2>OVERVIEW of LESSONS on Surface Area of Cylinders</H2>For your convenience, &nbsp;this file contains

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the list of my lessons on surface area of cylinders in this site,

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the major formulas for calculating the surface area of cylinders, &nbsp;and

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the list of relevant solved problems.

<H3>Major notions related to the surface area of cylinders</H3>Figures &nbsp;<B>1a</B>&nbsp; - &nbsp;<B>1e</B>&nbsp; illustrate the major notions related to the surface area of cylinders.

&nbsp;&nbsp;{{{drawing( 220, 225,  -5.5, 5.5, -6.0, 5.4,

ellipse( 1.0, -3.0, 8.0,  4.0),
            ellipse(-1.0,  2.0, 8.0,  4.0),
            line( -3.0, -3.0, -5.0,  2.0),
            line(  5.0, -3.0,  3.0,  2.0),

locate ( -5.4, -5.1, base),
            line ( -4.6, -5.0, -1.0, -3.5),

locate (  2.7,  5.3, lateral),
          locate (  2.7,  4.7, surface),
            line (  3.9,  3.9,  3.3, 0.5),

locate ( -5.4,  5.0, base),
            line ( -4.6,  4.1, -1.5, 2.5),

green(line ( 1.0, -3, -1.0,  2)),

circle ( 1.0, -3, 0.1, 0.1),
          locate ( 1.0, -2.4, O1),

circle (-1.0,  2, 0.1, 0.1),
          locate (-1.0,  2.6, O2)
)}}}

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1a</B>. Cylinder
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(general definition)

</TD>
  <TD>

&nbsp;&nbsp;{{{drawing( 220, 225,  -5.5, 5.5, -6.0, 5.4,

ellipse( 0.0, -3.0, 8.0,  4.0),
            ellipse( 0.0,  2.0, 8.0,  4.0),
            line( -3.92, -3.0, -3.92, 2.0),
            line(  4.0,  -3.0,  4.0,  2.0),

locate ( -5.4, -5.1, base),
            line ( -4.6, -5.0, -1.0, -3.5),

locate (  2.7,  5.3, lateral),
          locate (  2.7,  4.7, surface),
            line (  3.9,  3.9,  3.3, 0.5),

locate ( -5.4,  5.0, base),
            line ( -4.6,  4.1, -1.0, 2.5),

green(line ( 0.0, -3.5,  0.0,  2.5)),

circle ( 0.0,  -3, 0.1, 0.1),
          locate ( 0.15, -3.0, O1),

circle ( 0.0,   2, 0.1, 0.1),
          locate ( 0.15,  2.6, O2),

locate ( 4.15, 0.2, h),
          locate (-4.45, 0.2, h),

locate ( 3.3, -5.1, height),
      green(line ( 4.35, -4.9,  4.35, -0.6))
)}}}

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1b</B>. Right circular
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;cylinder

</TD>
  <TD>

&nbsp;&nbsp;{{{drawing( 440, 225,  -5.5, 16.5, -6.0, 5.4,

ellipse( 0.0, -3.0, 8.0,  4.0),
            ellipse( 0.0,  2.0, 8.0,  4.0),
            line( -3.92, -3.0, -3.92, 2.0),
            line(  4.0,  -3.0,  4.0,  2.0),

green(line(  0.0, 2.0, 2.7, 3.4)),
            locate(0.8, 3.3, r),

green(line( 0.0,  0.0, 15.5,  0.0)),
      green(line( 0.0, -5.0, 15.5, -5.0)),
      green(line( 0.0,  0.0,  0.0, -5.0)),
      green(line(15.5,  0.0, 15.5, -5.0)),

locate(7.0,  0.8, 2*pi*r),
            locate(5.0, -4.2, circumference=2*pi*r),

locate (-0.55, -2.2, h),
          locate (15.65, -2.2, h)
)}}}

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1c</B>. Right circular cylinder 
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and its flattening

</TD>
  <TD>
&nbsp;&nbsp;{{{drawing( 315, 225,  -0.5, 6.5, -2.5, 2.5,

line(  0.0,  0.5,  6.28,  0.5),
            line(  0.0, -0.5,  6.28, -0.5),

line(  0.0,  -0.5,  0.0,  0.5),
            line(  6.28, -0.5,  6.28, 0.5),

circle( 2.0,   1.5, 1, 1), 
           circle( 2.0,  -1.5, 1, 1) 
)}}}

&nbsp;&nbsp;<B>Figure 1d</B>. Flattening and the net of the  
&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;surface of a right circular cylinder

</TD>
 </TR>
</TABLE>

<H3>Major formulas for calculating the surface area of cylinders</H3><TABLE>
  <TR>
  <TD>

1. &nbsp;<B>The lateral surface area of a cylinder</B>&nbsp; is &nbsp;{{{S[lateral]}}} = &nbsp;{{{2pi}}}{{{r}}}{{{h}}},

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where &nbsp;{{{r}}}&nbsp; is the radius of the cylinder and &nbsp;{{{h}}}&nbsp; is its height.

2. &nbsp;<B>The total surface area</B>&nbsp; <B>S</B> &nbsp;<B>of a cylinder</B>&nbsp; is &nbsp;{{{S}}} = {{{S[lateral]}}} + {{{2S[base]}}} = {{{2pi}}}{{{r}}}{{{h}}} + {{{2}}}{{{pi}}}{{{r^2}}} = {{{2pi}}}{{{r}}}*(&nbsp;{{{h+r}}}&nbsp;),

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;where &nbsp;{{{S[lateral]}}}&nbsp; is the lateral surface area of the cylinder and &nbsp;{{{S[base]}}}&nbsp; is the cylinder base area.

</TD>
  <TD>

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(1)

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;(2)

</TD>
 </TR>
</TABLE>

<H3>My lessons on surface area of cylinders in this site</H3>&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-cylinders.lesson>Surface area of cylinders</A>

under the topic &nbsp;<B>Area and surface area</B>&nbsp; of the section &nbsp;<B>Geometry</B>, &nbsp;and

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-cylinders.lesson>Solved problems on surface area of cylinders</A>

under the topic &nbsp;<B>Geometry</B>&nbsp; of the section &nbsp;<B>Word problems</B>.

<H3>Solved problems on surface area of cylinders</H3>&nbsp;&nbsp;&nbsp;&nbsp;- Find the lateral surface area of a cylinder if the radius of the cylinder is of &nbsp;10 cm&nbsp; and the height of the cylinder is of &nbsp;5 cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then find the total surface area of the cylinder.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the lateral surface area of a cylinder if the radius of the cylinder is of &nbsp;5 cm&nbsp; and the height of the cylinder is of &nbsp;10 cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Then find the total surface area of the cylinder.

<TABLE>
  <TR>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Find the lateral surface area of a cylinder if the rectangular axial section of the cylinder has the area &nbsp;{{{a}}} = 100 {{{cm^2}}}.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;- Find the lateral surface area of a cylinder if the rectangular axial section of the cylinder has the area &nbsp;{{{a}}} = 10 {{{cm^2}}}.

&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a cone along its axis. &nbsp;The radius of the base of the cone is of &nbsp;5 cm&nbsp; and the height of

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the cone is of &nbsp;10 cm. &nbsp;The diameter of the hole is of &nbsp;4 cm. &nbsp;Find the surface area of the hole.

&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a cone along its axis. &nbsp;The radius of the base of the cone is of &nbsp;5 cm&nbsp; and the height of

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;the cone is of &nbsp;10 cm. &nbsp;The diameter of the hole is of &nbsp;2 cm. &nbsp;Find the surface area of the hole.

</TD>
  <TD>{{{drawing( 110, 114, -5.5, 5.5, -6.0, 5.4,

ellipse( 0.0, -3.0, 10.0,  6.0),
            ellipse( 0.0,  2.0, 10.0,  6.0),
            line( -5.0, -3.0, -5.0,  2.0),
            line(  5.0, -3.0,  5.0,  2.0),

blue(line( 0.0, 3.0, 0.0, -3.5)),

green(line(-4.6, -4,    4.1, -1.5)), 
      green(line(-4.6, -4,   -4.6,  0.9)), 
      green(line( 4.1, -1.5,  4.1,  3.5)), 
      green(line(-4.6,  0.9,  4.1,  3.5)) 
)}}}

</TD>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 110, 114, -5.5, 5.5, -6.0, 5.4,
      green(circle( 0, 0, 0.1, 0.1)),

ellipse( 0.0,  4.0,  4.0,  2.4),
      green(ellipse( 0.0, -3.0,  4.0,  2.4)),
            ellipse( 0.0, -3.0, 10.0,  6.0),
            line( 2.0,  4.0,  4.8, -2.2),
            line(-2.0,  4.0, -4.8, -2.2),

green(line( 2.0,  4.0,  2.0, -3.0)),
      green(line(-2.0,  4.0, -2.0, -3.0)),

blue(line( 0.0, 4.0, 0.0, -3.0))
)}}}

</TD>
 </TR>
</TABLE><TABLE>
  <TR>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a spherical solid body &nbsp;(in a ball)&nbsp; along its diameter. &nbsp;The radius of the ball is of &nbsp;5 cm&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the diameter of the hole is of &nbsp;4 cm. &nbsp;Find the surface area of the hole.

&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a spherical solid body &nbsp;(in a ball)&nbsp; along its diameter. &nbsp;The radius of the ball is of &nbsp;5 cm

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and the diameter of the hole is of &nbsp;2 cm. &nbsp;Find the surface area of the hole.

</TD>
  <TD>{{{drawing( 110, 110, -5.5, 5.5, -5.5, 5.5,
            circle( 0, 0, 5, 5),
      green(circle( 0, 0, 0.1, 0.1)),

green(locate (-0.2, -0.05, O)),

ellipse( 0.5,  3.0, 4.0, 2.4),
      green(ellipse(-0.5, -3.0, 4.0, 2.4)),
      green(line( -1.5, 3.0, -2.5, -3.0)),
      green(line(  2.5, 3.0,  1.5, -3.0))
)}}}

</TD>
 </TR>
</TABLE><TABLE>
  <TR>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Two cylinders are joined in a way that the base of one cylinder is overposed on the base of the other.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The radius of one cylinder is &nbsp;5 cm&nbsp; and the height is &nbsp;2 cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The radius of the other cylinder is &nbsp;2 cm&nbsp; and the height is &nbsp;5 cm. &nbsp;Find the surface area of the combined body.&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;- Two cylinders are joined in a way that the base of one cylinder is overposed on the base of the other.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The radius of one cylinder is &nbsp;5 cm&nbsp; and the height is &nbsp;2 cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The radius of the other cylinder is &nbsp;1 cm&nbsp; and the height is &nbsp;5 cm. &nbsp;Find the surface area of the combined body.

</TD>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 110, 114, -5.5, 5.5, -6.0, 5.4,

ellipse( 0.0, -3.0, 10.0,  6.0),
            ellipse( 0.0, -1.0, 10.0,  6.0),
            line( -5.0, -3.0, -5.0, -1.0),
            line(  5.0, -3.0,  5.0, -1.0),

ellipse( 0.0, -1.0,  4.0,  2.4),
            ellipse( 0.0,  4.0,  4.0,  2.4),

line( 2.0, -1.0,  2.0,  4.0),
            line(-2.0, -1.0, -2.0,  4.0),

blue(line( 0.0, 4.0, 0.0, -3.0)),

locate (-3.0, -1.5, 1),
            locate (-1.1,  2.9, 2)
)}}}

</TD>
 </TR>
</TABLE>

My lessons on surface area of cylinders and other 3D solid bodies in this site are

<TABLE>
  <TR>
  <TD>
<B>Lessons on surface area of prisms</B>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-prisms.lesson>Surface area of prisms</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-prisms.lesson>Solved problems on surface area of prisms</A>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/OVERVIEW-of-LESSONS-on-surface-area-of-prisms.lesson>Overview of lessons on surface area of prisms</A>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

</TD>
  <TD>
<B>Lessons on surface area of pyramids</B>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-pyramids.lesson>Surface area of pyramids</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-pyramids.lesson>Solved problems on surface area of pyramids</A>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/OVERVIEW-of-LESSONS-on-surface-area-of-pyramids.lesson>Overwiew of lessons on surface area of pyramids</A>

</TD>
 </TR>
</Table><TABLE>
  <TR>
  <TD>
<B>Lessons on surface area of cylinders</B>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-cylinders.lesson>Surface area of cylinders</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-cylinders.lesson>Solved problems on surface area of cylinders</A>

Overwiew of lessons on surface area of cylinders&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

</TD>
  <TD>
<B>Lessons on surface area of cones</B>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-cones.lesson>Surface area of cones</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-cones.lesson>Solved problems on surface area of cones</A>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/OVERVIEW-of-LESSONS-on-surface-area-of-cones.lesson>Overwiew of lessons on surface area of cones</A>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

</TD>
  <TD>
<B>Lessons on surface area of spheres</B>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/Surface-area-of-spheres.lesson>Surface area of spheres</A>

<A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-surface-area-of-spheres.lesson>Solved problems on surface area of spheres</A>

<A HREF=http://www.algebra.com/algebra/homework/Surface-area/OVERVIEW-of-LESSONS-on-surface-area-of-spheres.lesson>Overwiew of lessons on surface area of spheres</A>

</TD>
 </TR>
</Table>

To navigate over all topics/lessons of the Online Geometry Textbook use this file/link &nbsp;<A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>.