Lesson OVERVIEW of LESSONS on Volume of PRISMS
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<H2>OVERVIEW of LESSONS on Volume of Prisms</H2>For your convenience, this file contains - the list of my lessons on volume of prisms in this site, - the major formulas for calculating the volume of prisms, and - the list of relevant solved problems. <H3>Examples of prisms</H3>Figures <B>1a</B> - <B>1e</B> present the examples of prisms. <TABLE> <TR> <TD> {{{drawing( 200, 150, -4.0, 4.0, -0.5, 5.5, line ( 0.0, 0.0, 3.0, 0.0), line ( 0.0, 0.0, 0.0, 3.0), line ( 0.0, 0.0, -2.0, 0.8), line ( 0.0, 3.0, 3.0, 3.0), line ( 3.0, 3.0, 3.0, 0.0), line ( 0.0, 3.0, -2.0, 3.8), line ( -2.0, 3.8, 1.0, 3.8), line ( -2.0, 3.8, -2.0, 0.8), green(line ( 1.0, 3.8, 1.0, 0.8)), line ( 1.0, 3.8, 3.0, 3.0), green(line ( -2.0, 0.8, 1.0, 0.8)), green(line ( 1.0, 0.8, 3.0, 0.0)), locate( 1.2, 0.1, a), locate(-1.5, 0.6, a), locate(-0.4, 2.1, a) )}}} <B>Figure 1a</B>. A cube </TD> <TD> {{{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), green(line ( -0.5, 4.5, -0.5, 1.5)), line ( -0.5, 4.5, 4.0, 3.0), green(line ( -4.0, 1.5, -0.5, 1.5)), green(line ( -0.5, 1.5, 4.0, 0.0)), locate( 1.7, 0.05, u), locate(-2.3, 0.80, v), locate( 0.15, 2.20, w) )}}} <B>Figure 1b</B>. A rectangular prism </TD> <TD> {{{drawing( 225, 225, -4.0, 5.0, -0.5, 8.5, line ( 0.0, 0.0, 4.0, 0.0), line ( 0.0, 0.0, 0.0, 7.0), line ( 0.0, 0.0, -3.0, 1.5), line ( 4.0, 7.0, 4.0, 0.0), line ( 4.0, 7.0, 0.0, 7.0), line ( -3.0, 8.5, -3.0, 1.5), line ( -3.0, 8.5, 0.0, 7.0), line ( -3.0, 8.5, 4.0, 7.0), green(line ( -3.0, 1.5, 4.0, 0.0)) )}}} <B>Figure 1c</B>. A triangular prism </TD> <TD> {{{drawing( 225, 225, -4.0, 5.0, -0.5, 8.5, line ( 0.0, 0.0, 4.0, 0.0), line ( 0.0, 0.0, -3.0, 1.5), green(line ( -3.0, 1.5, 2.0, 2.0)), green(line ( 2.0, 2.0, 4.0, 0.0)), line ( 0.0, 6.0, 4.0, 6.0), line ( 0.0, 6.0, -3.0, 7.5), line ( -3.0, 7.5, 2.0, 8.0), line ( 2.0, 8.0, 4.0, 6.0), line ( 0.0, 0.0, 0.0, 6.0), line ( -3.0, 1.5, -3.0, 7.5), green(line ( 2.0, 2.0, 2.0, 8.0)), line ( 4.0, 0.0, 4.0, 6.0) )}}} <B>Figure 1d</B>. A quadrilatelar prism </TD> <TD> {{{drawing( 238, 232, -2.5, 7.0, -0.5, 8.6, line ( 0.0, 0.0, 4.0, 0.0), line ( 0.0, 0.0, -1.7, 1.5), green(line ( -1.7, 1.5, 1.0, 2.3)), green(line ( 1.0, 2.3, 4.5, 2.3)), green(line ( 4.5, 2.3, 6.5, 1.0)), line ( 6.5, 1.0, 4.0, 0.0), line ( 0.0, 6.0, 4.0, 6.0), line ( 0.0, 6.0, -1.7, 7.5), line ( -1.7, 7.5, 1.0, 8.3), line ( 1.0, 8.3, 4.5, 8.3), line ( 4.5, 8.3, 6.5, 7.0), line ( 6.5, 7.0, 4.0, 6.0), line ( 0.0, 0.0, 0.0, 6.0), line ( -1.7, 1.5, -1.7, 7.5), green(line ( 1.0, 2.3, 1.0, 8.3)), green(line ( 4.5, 2.3, 4.5, 8.3)), line ( 6.5, 1.0, 6.5, 7.0), line ( 4.0, 0.0, 4.0, 6.0) )}}} <B>Figure 1e</B>. A hexagonal prism </TD> </TR> </TABLE> <H3>Major formulas for calculating the volume of prisms</H3> 1. <B>Volume</B> <B>V</B> <B>of a <U>cube</U></B> with the edge measure <B>a</B> is {{{V}}} = {{{a^3}}}. 2. <B>Volume</B> <B>V</B> <B>of a <U>rectangular prism</U></B> with the edge measures <B>u</B>, <B>v</B> and <B>w</B> is {{{V}}} = {{{uvw)}}}. 3. <B>Volume</B> <B>V</B> <B>of an <U>upright prism</U></B> is {{{V}}} = {{{S*h}}}, where <B>S</B> is the area of the prism base and <B>h</B> is the prism height. <H3>My lessons on volume of prisms in this site</H3> - <A HREF=http://www.algebra.com/algebra/homework/Volume/-Volume-of-prisms.lesson>Volume of prisms</A> under the topic <B>Volume, metric volume</B> of the section <B>Geometry</B>, and - <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-volume-of-prisms.lesson>Solved problems on volume of prisms</A> under the topic <B>Geometry</B> of the section <B>Word problems</B>. <H3>Solved problems on volume of prisms</H3>Lesson <A HREF=http://www.algebra.com/algebra/homework/Volume/-Volume-of-prisms.lesson>Volume of prisms</A> - Find the volume of a cube with the edge measure of 5 cm. - Find the volume of a rectangular prism which has the edge measures of 8 cm, 10 cm and 6 cm. - Find the volume of a triangular prism if its base is an equilateral triangle with the side measure of 4 cm and the height of the prism is of 10 cm. - Find the volume of a hexagonal prism if its base is a regular hexagon with the side measure of 4 cm and the height of the prism is of 10 cm. Lesson <A HREF=http://www.algebra.com/algebra/homework/word/geometry/Solved-problems-on-volume-of-prisms.lesson>Solved problems on volume of prisms</A> - Find the volume of a rectangular prism which has the edge measures of 4 cm, 5 cm and 3 cm. - Find the volume of a triangular prism if its base is a right-angled triangle with the leg measures of 3 cm and 4 cm, and the height of the prism is of 10 cm. - Find the volume of a triangular prism if the side measures of the triangle at the base are of 13 cm, 14 cm and 15 cm, and the height of the prism is of 20 cm. - Find the volume of a triangular prism if its base is an equilateral triangle with the side measure of 6 cm and the height of the prism is of 10 cm. - Find the volume of a hexagonal prism if its base is a regular hexagon with the side measure of 6 cm, and the height of the prism is of 10 cm. My lessons on volume of prisms and other 3D solid bodies in this site are <TABLE> <TR> <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> Overview of lessons on volume of prisms </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> </TD> </TR> </Table><TABLE> <TR> <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> <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> </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> </TD> <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> </TD> </TR> </Table> To navigate over all topics/lessons of the Online Geometry Textbook use this file/link <A HREF=https://www.algebra.com/algebra/homework/Triangles/GEOMETRY-your-online-textbook.lesson>GEOMETRY - YOUR ONLINE TEXTBOOK</A>.
