Lesson OVERVIEW of LESSONS on Volume of CONES

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

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

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

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

The &nbsp;<B>Figure 1</B>&nbsp; shows an example of a cone.

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

ellipse( 0.0, -3.0, 8.0,  4.0),
            line( -3.9, -2.8,  0.0,  5.0),
            line(  4.0, -2.8,  0.0,  5.0),

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

circle ( 0.0, -3, 0.1, 0.1),
          locate (-0.2, -3.1, O),

green(line (0.0, 5.0, 0.0, -3.0)),
          locate (0.15, 0.9, h),
          locate (0.15, 0.3, height),

locate (2.10, 2.1, l),
          locate (2.70, 2.1, -slant),
          locate (3.25, 1.5, height),

green(line ( 0.0, -3.0,  2.5, -1.5)),
          locate (1.3, -2.0, r)
)}}}

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;<B>Figure 1</B>. A cone

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<H3>Formula for calculating the volume of cones</H3>
<B>The volume of a cone</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 cones in this site</H3>&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Volume/Volume-of-cones.lesson>Volume of cones</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-cones.lesson>Solved problems on volume of cones</A>

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

<H3>Solved problems on volume of cones</H3>&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a cone if the base radius of the cone is of &nbsp;5 cm&nbsp; and the height of the cone is of &nbsp;10 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a cone if the base radius of the cone is of &nbsp;4 cm&nbsp; and the height of the cone is of &nbsp;9 cm.

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a composite solid body which comprises of two identical cones joined base to base, &nbsp;if their&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;common base radius is of &nbsp;3 cm&nbsp; and the height is of &nbsp;4 cm&nbsp; each.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a composite solid body which comprises of two identical cones joined base to base, &nbsp;if their

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;common base radius is of &nbsp;4 cm&nbsp; and the height is of &nbsp;3 cm&nbsp; each.

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 105, 125,  -3.5, 3.5, -3.8, 4.5,

ellipse (0.0, 0.0, 6.0, 3.0),

line ( -2.74, 0.5,  0.0,  3.9),
            line (  2.80, 0.5,  0.0,  3.9),

line ( -2.80, -0.5,  0.0, -3.5),
            line (  2.85, -0.5,  0.0, -3.5)
)}}}

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- A composite solid body comprises of the cone and the cylinder that have the same base radius measure.&nbsp; The cone &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 the cylinder are joined base to base in a way that the centers of their bases coincide. &nbsp;Find the volume

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of the given body if the common base radius is of &nbsp;3 cm&nbsp; and the height of the cone and the cylinder is of &nbsp;4 cm.

&nbsp;&nbsp;&nbsp;&nbsp;- A composite solid body comprises of the cone and the cylinder that have the same base radius measure.&nbsp; The cone &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 the cylinder are joined base to base in a way that the centers of their bases coincide. &nbsp;Find the volume

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;of the given body if the common base radius is of &nbsp;4 cm&nbsp; and the height of the cone and the cylinder is of &nbsp;3 cm.

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 105, 150,  -3.5, 3.5, -5.5, 4.5,

ellipse (0.0, 0.0, 6.0, 2.0),

line ( -2.68, 0.5,  0.0,  3.9),
            line (  2.73, 0.5,  0.0,  3.9),

ellipse (0.0, -4.0, 6.0, 2.0),

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

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a body &nbsp;(a truncated cone)&nbsp; obtained from a cone with the base radius of &nbsp;6 cm and the 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;of &nbsp;8 cm&nbsp; after cutting off the part of the cone by the plane parallel to the base in a way that the cutting plane

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;bisects the height of the original cone.

&nbsp;&nbsp;&nbsp;&nbsp;- Find the volume of a body &nbsp;(a truncated cone)&nbsp; obtained from a cone with the base radius of &nbsp;4 cm and the 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;of &nbsp;6 cm&nbsp; after cutting off the part of the cone by the plane parallel to the base in a way that the cutting plane

&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;bisects the height of the original cone.

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  <TD>&nbsp;&nbsp;&nbsp;&nbsp;{{{drawing( 105, 125,  -3.5, 3.5, -3.8, 4.5,

ellipse (0.0, -2.0, 6.0, 3.0),

ellipse (0.0,  1.0, 3.0, 1.5),

line ( -2.75, -1.5,  -1.375,  1.25),
            line (  2.82, -1.5,   1.410,  1.25),

green(line ( -1.375,  1.25,  0.0,  4.0)),
      green(line (  1.410,  1.25,  0.0,  4.0)),

green(line (0, -2, 0, 4))
)}}}

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

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<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;

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<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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<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>

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

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<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>

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

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<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>.