GA - Volume Lesson

Volume

In sixth grade, you learned to find the volumes of rectangular prisms. In this lesson, you will use the math you already know to solve problems involving volume of composed figures. Remember that the formula for finding volume is the same for all shapes:

V = Bh (where B is the area of the base and h is the height of the shape)

When you find the area of composite figures, you add the areas to get the area of the total shape. When you find the volume of composed figures, you add the volumes of each shape to get the total volume. Volume is always measured in cubic units.

Start with a rectangular prism:

rectangular prisms with sides 7 in, 7 in, 12 in

Use the formula V = Bh and insert the dimensions.

V = (7x7)12

V=(49)12

V=588 equation image indicator LaTeX: in^3 $in^3$

Try it with a triangular prism:

triangular prism with sizes 22 m, 13m, base 8m, height 11m

Use the formula V = Bh and insert the dimensions.

$LaTeX: V=\left(\frac{1}{2}bh\right)h$ $V=\left(\frac{1}{2}bh\right)h$ equation image indicator (area of the triangle times the height of the prism)

$LaTeX: V=\frac{1}{2}\left(8\cdot11\right)22$ $V=\frac{1}{2}\left(8\cdot11\right)22$

V = 44*22

V=968 equation image indicator LaTeX: ft^3 $ft^3$

Time for a trapezoidal prism:

trapezoidal prism with measurements of 8 ft, 18ft, 11 ft, 5 ft, and height of 10 ft

Use the formula V = Bh and insert the dimensions.

$LaTeX: V=\frac{1}{2}h\left(b_1+b_2\right)\cdot h$ $V=\frac{1}{2}h\left(b_1+b_2\right)\cdot h$ equation image indicator (area of the trapezoid times the height of the prism)

equation image indicator $LaTeX: V=\frac{1}{2}10\left(5+11\right)18$ $V=\frac{1}{2}10\left(5+11\right)18$

V = 80 * 18

LaTeX: V=1440m^3 $V=1440m^3$

It is time to put our knowledge of calculating volume into solving a problem with composed shapes. Many buildings are composed of a rectangular prism and a triangular prism. Solve the problem below:

building measurements of 3.5 ft, 4 ft, 2 ft, 2.5 ft, and 3 ft

Mr. Stringer is building a garage for his toddler's toy car. What is the volume of the garage?

Roof(triangular Prism)

3.5 x 3 = 10.5

10.5/2 = 5.25

5.25 x 4 = 21 cubic ft

Base(Rectangular Prism)

3.5 x 4 = 14

14 x 2 = 28

28 cubic ft

The garage has a volume of 49 cubic feet

Watch these two short videos to learn more about finding volume of 3D figures.

Volume Practice

Volume Homework

Now that you have spent some time learning strategies for solving problems with volume of prisms and composed figures, you are ready to complete your Geometric Applications: Volume Homework. Download your homework by CLICKING HERE. Links to an external site.

Once you have completed your homework, AND MAKE SURE YOU ATTEMPTED AND WORKED THE PROBLEMS OUT ON YOUR OWN, click here to download your homework key. Links to an external site.

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