6th Grade Volume of Prisms with Fractional Edges Lesson (Free PDF)
This volume fractions lesson for 6th Grade covers volume of prisms with fractional edges (Common Core 6.G.A.2), with a free PDF to print.
The volume of a right rectangular prism is the product of its length, width, and height, V = lwh, or the base area times the height, V = Bh. Volume is measured in cubic units. It works with fractional edges too: a 2 by 1 1/2 by 1 prism holds 24 cubes of edge 1/2, so its volume is 3.
Grade 6 · Common Core State Standards: 6.G.A.2
Key facts in this volume fractions lesson
- Volume is the number of cubic units that fill a solid.
- V = lwh or V = Bh for a right rectangular prism.
- Fractional edges work the same way: multiply the fractions.
- A cube with edge 1/2 has volume 1/8, and 8 of them fill a unit cube.
- To find a missing edge, divide the volume by the product of the other edges.
What is volume?
Volume measures the space inside a solid. It is counted in cubic units. A cube with edge 1 unit has a volume of 1 cubic unit. A prism that is 4 units long, 3 units wide, and 2 units tall holds 2 layers of \(4 \cdot 3 = 12\) cubes, which is 24 cubes.
How do you find volume with fractional edges?
Fill the prism with cubes whose edges are a fraction of a unit. A cube with edge \(\frac{1}{2}\) unit has volume \(\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}\) cubic unit. A prism that is 2 units by \(1\frac{1}{2}\) units by 1 unit is filled by \(4 \cdot 3 \cdot 2 = 24\) such cubes, so its volume is \(24 \cdot \frac{1}{8} = 3\) cubic units.
The same answer comes from multiplying the edge lengths: \(2 \cdot \frac{3}{2} \cdot 1 = 3\). This works for any fractional edges, so you can use \(V = \ell wh\) directly.
How do you solve volume problems?
- Draw or picture the prism and label the edges.
- Write the formula and substitute the lengths (use fractions or mixed numbers).
- Multiply and write the unit as cubic units.
- For a missing edge, divide the volume by the product of the other edges.
Example: A tank is \(1\frac{1}{2}\) ft by 2 ft by \(1\frac{1}{2}\) ft. Its volume is \(\frac{3}{2} \cdot 2 \cdot \frac{3}{2} = \frac{9}{2} = 4\frac{1}{2}\) cubic feet.
Volume fractions lesson: questions and answers
What is the formula for the volume of a rectangular prism?
The volume is V = length times width times height, or the area of the base times the height.
How do you find volume with fractional edge lengths?
Multiply the fractions or mixed numbers. For a prism 1 1/2 by 2 by 4, the volume is 3/2 times 2 times 4, which is 12.
Why are volume units cubic?
Volume counts cubes that fill the space, so the unit is a cube, such as cubic inches or cubic feet.
How do you find a missing height?
Divide the volume by the base area. If V = 60 and the base area is 12, then h = 60 divided by 12 = 5.
What is the volume of a cube with edge 1/2 unit?
It is (1/2) times (1/2) times (1/2), which is 1/8 cubic unit. Eight of these cubes fill one unit cube.
How to use this volume fractions lesson
Read the definitions first, then follow the worked method line by line and redo the example on paper without looking. When every step makes sense, move on to the worksheet, then check yourself with the quiz.
Download the volume fractions lesson as a PDF with the button below and keep it with your notes.
All Grade 6 chapters: Grade 6 math.
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