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Mathematics LibreTexts

5.A: Volume

  • Page ID
  • \( \newcommand{\vecs}[1]{\overset { \scriptstyle \rightharpoonup} {\mathbf{#1}} } \) \( \newcommand{\vecd}[1]{\overset{-\!-\!\rightharpoonup}{\vphantom{a}\smash {#1}}} \)\(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\) \(\newcommand{\id}{\mathrm{id}}\) \( \newcommand{\Span}{\mathrm{span}}\) \( \newcommand{\kernel}{\mathrm{null}\,}\) \( \newcommand{\range}{\mathrm{range}\,}\) \( \newcommand{\RealPart}{\mathrm{Re}}\) \( \newcommand{\ImaginaryPart}{\mathrm{Im}}\) \( \newcommand{\Argument}{\mathrm{Arg}}\) \( \newcommand{\norm}[1]{\| #1 \|}\) \( \newcommand{\inner}[2]{\langle #1, #2 \rangle}\) \( \newcommand{\Span}{\mathrm{span}}\)\(\newcommand{\AA}{\unicode[.8,0]{x212B}}\)


    The purpose of this lesson is to learn how to find the volume of various solids.

    This lesson will address the following CCRS Standard(s) for Geometry:

    • 7.G.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three- dimensional objects composed of triangles, quadrilaterals, polygons, cubes, and right prisms
    • G.GMD.3: Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems
    • G.MG.2: Apply concepts of density based on area and volume in modeling situations (e.g. persons per square mile, BTUs per cubic foot)


    1. Take notes while watching videos below
    2. Go to and log into our course to complete assignment 5.A with 80% or better.


    Complete assignment 5.A with 80% or better at


    In this lesson we have learned:

    • If B is the area of the base, then the volume of the prism or cylinder is LaTeX: V=Bh
    • If B is the area of the base, then the volume of the pyramid or cone is LaTeX: V=\frac{1}{3}Bh
    • The volume of a sphere is LaTeX: V=\frac{4}{3}\pi r^3</mi> <msup> <mi>r</mi> <mn>3</mn> </msup> </math>' data-equation-content="V=\frac{4}{3}\pi r^3">

    5.A: Volume is shared under a not declared license and was authored, remixed, and/or curated by LibreTexts.

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