Lesson OVERVIEW of LESSONS on Volume of CYLINDERS

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

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

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;- the formula for calculating the volume of cylinders, &nbsp;and

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

<H3>Major notions related to the volume of cylinders</H3>Figures &nbsp;<B>1a</B>&nbsp; and  &nbsp;<B>1b</B>&nbsp; illustrate the major notions related to the volume 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 ( -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;&nbsp;&nbsp;&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 ( -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;&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;&nbsp;&nbsp;&nbsp;&nbsp;cylinder

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 </TR>
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<H3>Formula for calculating the volume of cylinders</H3>
<B>The volume of a cylinder</B>&nbsp; is &nbsp;{{{V}}} = &nbsp;{{{pi}}}{{{r^2}}}{{{h}}} = {{{S[base]}}}{{{h}}},

where &nbsp;{{{r}}}&nbsp; is the radius of the cylinder, &nbsp;{{{h}}}&nbsp; is its height, &nbsp;and &nbsp;{{{S[base]}}}= {{{pi}}}{{{r^2}}}&nbsp; is the base area &nbsp;(the area of the circle at the base).

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

under the topic &nbsp;<B>Volume, metric volume</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-volume-of-cylinders.lesson>Solved problems on volume of cylinders</A>

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

<H3>Solved problems on volume of cylinders</H3>&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a cylinder if the radius of the cylinder is of &nbsp;5 cm&nbsp; and the height of the cylinder is of &nbsp;4 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a cylinder if the radius of the cylinder is of &nbsp;4 cm&nbsp; and the height of the cylinder is of &nbsp;5 cm.

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  <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 volume of the composite 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;&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;10 cm&nbsp; and the height is &nbsp;4 cm.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;The radius of the other cylinder is &nbsp;4 cm&nbsp; and the height is &nbsp;10 cm. &nbsp;Find the volume of the composite 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)
)}}}

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 </TR>
</TABLE>

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  <TR>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of the solid body concluded between two co-axial cylindrical  surfaces of the radii of &nbsp;10 cm&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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and &nbsp;5 cm&nbsp; respectively if the common height of the two cylindrical shells is of &nbsp;8 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of the solid body concluded between two co-axial cylindrical  surfaces of the radii of &nbsp;8 cm

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;and &nbsp;4 cm&nbsp; respectively if the common height of the two cylindrical shells is of &nbsp;10 cm.

</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, -3.0, 10.0,  4.0),
            ellipse( 0.0,  3.0, 10.0,  4.0),

ellipse( 0.0,  3.0,  4.0,  1.6),
      green(ellipse( 0.0, -3.0,  4.0,  1.6)),
            line( 5.0,  3.0,  5.0, -3.0),
            line(-5.0,  3.0, -5.0, -3.0),

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

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

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 </TR>
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  <TR>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Four through cylindrical holes are made in the solid cylinder parallel to its axis of symmetry.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the volume of the obtained solid body if the diameter of the original cylinder is &nbsp;10 cm, &nbsp;its height&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;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is &nbsp;8 cm&nbsp; and the diameter of each hole is &nbsp;2 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- Four through cylindrical holes are made in the solid cylinder parallel to its axis of symmetry.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the volume of the obtained solid body if the diameter of the original cylinder is &nbsp;20 cm, &nbsp;its height

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;is &nbsp;16 cm&nbsp; and the diameter of each hole is &nbsp;4 cm.

</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,  3.0, 10.0,  4.0),
            ellipse( 0.0, -3.0, 10.0,  4.0),
            line( 5.0,  3.0,  5.0, -3.0),
            line(-5.0,  3.0, -5.0, -3.0),

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

ellipse( 2.5,  2.2,  2.0,  0.8),
      green(ellipse( 2.5, -3.8,  2.0,  0.8)),

green(line( 1.5,  2.2,  1.5, -3.8)),
      green(line( 3.5,  2.2,  3.5, -3.8)),

blue(line( 2.5, 2.2,  2.5, -3.8)),

ellipse( 2.5,  3.8,  2.0,  0.8),
      green(line( 1.5,  3.8,  1.5,  2.6)),
      green(line( 3.5,  3.8,  3.5,  2.6)),

blue(line( 2.5, 3.8,   2.5,  3.0))

ellipse(-2.5,  2.2,  2.0,  0.8),
      green(ellipse(-2.5, -3.8,  2.0,  0.8)),

green(line(-1.5,  2.2, -1.5, -3.8)),
      green(line(-3.5,  2.2, -3.5, -3.8)),

blue(line(-2.5, 2.2, -2.5, -3.8)),

ellipse(-2.5,  3.8,  2.0,  0.8),
      green(line(-1.5,  3.8, -1.5,  2.6)),
      green(line(-3.5,  3.8, -3.5,  2.6)),

blue(line(-2.5, 3.8,  -2.5,  3.0))
)}}}

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a rectangular prism &nbsp;(rectangular box)&nbsp; of dimensions &nbsp;6x8x10 cm&nbsp; along&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;&nbsp;&nbsp;&nbsp;its axis of symmetry parallel to the shortest edge.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the volume of the obtained solid body if the diameter of the hole is &nbsp;2 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- A through cylindrical hole is made in a rectangular prism &nbsp;(rectangular box)&nbsp; of dimensions &nbsp;3x4x5 cm&nbsp; along

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;its axis of symmetry parallel to the shortest edge.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the volume of the obtained solid body if the diameter of the hole is &nbsp;2 cm.

</TD>
  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 250, 150,  -5.0, 5.0, -0.5, 5.5,

line (  0.0, 0.0,  4.0,  0.0),
            line (  0.0, 0.0,  0.0,  3.0),
            line (  0.0, 0.0, -4.0,  1.5),

line (  0.0, 3.0,  4.0,  3.0),
            line (  4.0, 3.0,  4.0,  0.0),

line (  0.0, 3.0, -4.0,  4.5),
            line ( -4.0, 4.5, -4.0,  1.5),
            line ( -4.0, 4.5, -0.5,  4.5),
            line ( -4.0, 4.5, -4.0,  1.5),

line ( -0.5, 4.5,  4.0,  3.0),

ellipse(-0.2, 3.7, 1.0, 0.3),
      green(ellipse(-0.2, 0.7, 1.0, 0.3)),
      green(line ( -0.7, 3.7, -0.7,  0.7)),
      green(line (  0.3, 3.7,  0.3,  0.7)),

green(line ( -4.0, 1.5, -1.0, 1.5)),
      green(line ( -0.5, 4.5, -0.5, 4.0)),
      green(line (  4.0, 0.0,  0.4, 1.2))
)}}}

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

&nbsp;&nbsp;&nbsp;&nbsp;- A pie, &nbsp;which has a cylindrical shape, &nbsp;is cut in &nbsp;8&nbsp; equal sectorial pieces along the radii.

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;Find the volume of each piece if the diameter of the original pie is of &nbsp;10 inches&nbsp; and its height is of&nbsp; 2 inches.

&nbsp;&nbsp;&nbsp;&nbsp;- A swimming pool has a cylindrical shape. &nbsp;Find the volume of the pool if its diameter is of &nbsp;40 ft&nbsp; and the depth is of &nbsp;8 ft.

&nbsp;&nbsp;&nbsp;&nbsp;- An oil storage tank has a cylindrical shape. &nbsp;Find the volume of the storage tank if its diameter is of &nbsp;60 m&nbsp; and the height is of &nbsp;20 m.

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

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  <TD>
<B>Lessons on volume of prisms</B>

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

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

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

</TD>
  <TD>
<B>Lessons on volume of pyramids</B>

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

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

<A HREF=http://www.algebra.com/algebra/homework/Volume/OVERVIEW-of-LESSONS-on-volume-of-pyramids.lesson>Overview of lessons on volume of pyramids</A>

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</Table><TABLE>
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  <TD>
<B>Lessons on volume of cylinders</B>

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

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

Overview of lessons on volume of cylinders&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

</TD>
  <TD>
<B>Lessons on volume of cones</B>

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

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

<A HREF=http://www.algebra.com/algebra/homework/Volume/OVERVIEW-of-LESSONS-on-Volume-of-cones.lesson>Overview of lessons on volume of cones</A>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;

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  <TD>
<B>Lessons on volume of spheres</B>

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

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

<A HREF=http://www.algebra.com/algebra/homework/Volume/OVERVIEW-of-LESSONS-on-Volume-of-spheres.lesson>Overview of lessons on volume of spheres</A>

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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>.