6th Grade Volume of Prisms with Fractional Edges Worksheet Solutions (PDF)

6th Grade math worksheet solutions: Volume of Prisms with Fractional Edges – Maths PDF

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This volume fractions answers for 6th Grade covers volume of prisms with fractional edges (Common Core 6.G.A.2), with a free PDF to print.

Check each volume here. The solutions write the formula, substitute the edge lengths, and give the final answer in cubic units in bold. Prism diagrams show unit cubes and fractional cubes for several problems.

Grade 6 · Common Core State Standards: 6.G.A.2

Volume fractions answers: exercises 1 to 10

Exercise 1 – Volume with unit cubes

$V = \ell \cdot w \cdot h = 5 \cdot 3 \cdot 4 = 60$

$60\text{ in}^{3}$

Exercise 2 – Volume of a cube

$V = 3 \cdot 3 \cdot 3 = 27$

$27\text{ in}^{3}$

Exercise 3 – One fractional edge

$V = \frac{3}{2} \cdot 2 \cdot 4 = 3 \cdot 4 = 12$

$12\text{ ft}^{3}$

Exercise 4 – Packing with half-unit cubes

Cubes: $4 \cdot 3 \cdot 2 = 24$.

One cube: $\frac{1}{2} \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{8}$.

$24 \cdot \frac{1}{8} = 3$. Check: $2 \cdot \frac{3}{2} \cdot 1 = 3$.

$3\text{ units}^{3}$

Exercise 5 – Volume with all fractions

$V = \frac{1}{2} \cdot \frac{3}{4} \cdot 4 = \frac{3}{8} \cdot 4 = \frac{3}{2} = 1\frac{1}{2}$

$1\frac{1}{2}\text{ m}^{3}$

Exercise 6 – Base times height

$V = 12 \cdot 5 = 60$

$60\text{ ft}^{3}$

Exercise 7 – Fractional base area

$V = \frac{3}{4} \cdot 8 = 6$

$6\text{ m}^{3}$

Exercise 8 – Find the missing height

$36 = 4 \cdot 3 \cdot h = 12h$.

$h = 36 \div 12 = 3$

3 centimeters

Exercise 9 – Find the missing length

$45 = \ell \cdot 3 \cdot 5 = 15\ell$.

$\ell = 45 \div 15 = 3$

3 inches

Exercise 10 – Fish tank

$V = 24 \cdot 10 \cdot 12 = 2880$

$2{,}880\text{ in}^{3}$

A tank with volume 2,880 cubic inches.

Exercises 11 and up

Exercise 11 – Mixed number edges

$V = \frac{5}{2} \cdot 3 \cdot \frac{3}{2} = \frac{45}{4} = 11\frac{1}{4}$

$11\frac{1}{4}\text{ ft}^{3}$

Exercise 12 – Partly filled tank

Full tank: $\frac{3}{2} \cdot 2 \cdot \frac{3}{2} = \frac{9}{2}$.

Water: $\frac{3}{4} \cdot \frac{9}{2} = \frac{27}{8} = 3\frac{3}{8}$

$3\frac{3}{8}\text{ ft}^{3}$

Three fourths of the full tank.

Exercise 13 – Same volume

A: $4 \cdot 3 \cdot 2 = 24$. B: $2 \cdot 2 \cdot 6 = 24$.

Both have a volume of 24 cubic feet (equal).

Exercise 14 – Boxes in a crate

Crate: $4 \cdot 2 \cdot 3 = 24$ cubic feet.

Box: $1 \cdot \frac{1}{2} \cdot \frac{1}{2} = \frac{1}{4}$ cubic foot.

$24 \div \frac{1}{4} = 96$

96 boxes

Exercise 15 – Sandbox

$V = 6 \cdot 4 \cdot \frac{1}{2} = 12$ cubic feet.

Cost: $\$5.00 \cdot 12 = \$60.00$.

$12\text{ ft}^{3}$; $60.00

Exercise 16 – Cubes of half a unit

Box: $3 \cdot 2 \cdot 1 = 6$. Cube: $\frac{1}{8}$.

$6 \div \frac{1}{8} = 48$.

Check by counting: 6 cubes along the length, 4 along the width, and 2 along the height give $6 \cdot 4 \cdot 2 = 48$.

48 cubes

Each cube has an edge of 1/2 inch.

Exercise 17 – Butter block

$\frac{7}{2} \cdot \frac{3}{2} \cdot \frac{3}{2} = \frac{63}{8} = 7\frac{7}{8}$

$7\frac{7}{8}\text{ in}^{3}$

Exercise 18 – Planter box

Volume: $3 \cdot \frac{3}{2} \cdot 2 = 9$ cubic feet.

$9 \div 3 = 3$

3 bags

Three bags of 3 cubic feet fill the box.

Exercise 19 – Three fractions

$V = \frac{3}{4} \cdot \frac{2}{3} \cdot \frac{1}{2} = \frac{6}{24} = \frac{1}{4}$

$\frac{1}{4}\text{ in}^{3}$

Exercise 20 – Multi-step volume

Bottom: $4 \cdot 3 \cdot \frac{3}{2} = 18$. Top: $4 \cdot 3 \cdot 2 = 24$.

Total volume $18 + 24 = 42$. Total height $1\frac{1}{2} + 2 = 3\frac{1}{2}$. Check: $4 \cdot 3 \cdot 3.5 = 42$.

$42\text{ ft}^{3}$; $3\frac{1}{2}$ ft

Key facts behind this volume fractions answers

Key facts

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.

How to use this volume fractions answers

Cover each solution, solve the exercise again, then uncover it and compare every line. If your answer differs, find the first step that changed and redo the exercise from there.

Download the volume fractions answers as a PDF with the button below and keep it with your notes.

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