5th Grade Volume of Rectangular Prisms Worksheet Solutions (PDF)

5th Grade math worksheet solutions: Volume of Rectangular Prisms – Maths PDF

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This volume practice solutions for 5th Grade covers volume of rectangular prisms (Common Core 5.MD.C.3, 5.MD.C.4, 5.MD.C.5), with a free PDF to print.

Each answer shows the layers or the formula, the multiplication, and the final volume with cubic units. For composite solids, check that you added the two volumes.

Grade 5 · Common Core State Standards: 5.MD.C.3, 5.MD.C.4, 5.MD.C.5

Volume practice solutions: exercises 1 to 10

Exercise 1 – Count the cubes

One layer has $3\times2=6$ cubes. There are 2 layers.

$6\times2=12$.

12 cubic units

Exercise 2 – Layers of cubes

(a) $4\times3=12$ cubes per layer.

(b) 3 layers.

A rectangular prism.

36 cubic units

Exercise 3 – Volume in cubic feet

Use $V=l\times w\times h$.

$V=5\times3\times2=30$.

$30\text{ ft}^{3}$

Exercise 4 – Volume in cubic centimeters

Use $V=l\times w\times h$.

$V=6\times4\times5=120$.

$120\text{ cm}^{3}$

Exercise 5 – Volume in cubic inches

Use $V=l\times w\times h$.

$V=8\times2\times7=112$.

$112\text{ in}^{3}$

Exercise 6 – Base area times height

Use $V=B\times h$.

$V=24\times5=120$.

120 cubic units

Exercise 7 – Using the base area

$V=B\times h=18\times4=72$.

$72\text{ in}^{3}$

Exercise 8 – Find the height

Base area: $6\times5=30$ square cm.

$30\times h=90$, so $h=90\div30=3$.

Check: $6\times5\times3=90$.

3 cm

Exercise 9 – Find the missing edge

$15\times h=105$, so $h=105\div15=7$.

7 ft

Exercise 10 – Volume of a cube

A cube has equal edges, so $V=4\times4\times4=64$.

$64\text{ m}^{3}$

Exercises 11 and up

Exercise 11 – Prism from a picture

Base: $5\times2=10$ cubes. Height: 3 layers.

$10\times3=30$.

30 cubic units

Exercise 12 – Fish tank

$20\times10=200$ is the base area.

$200\times12=2{,}400$.

$2{,}400\text{ in}^{3}$

Exercise 13 – Compare two boxes

Box A: $3\times7\times4=84$. Box B: $6\times5\times3=90$.

$90-84=6$.

Box B is greater by $6\text{ in}^{3}$

Exercise 14 – Two prisms joined

Prism A: $4\times3\times2=24$. Prism B: $2\times3\times1=6$.

$24+6=30$.

A composite solid made of prism A and prism B.

30 cubic units

Exercise 15 – Step-shaped solid

Prism A: $7\times4\times3=84$. Prism B: $3\times4\times2=24$.

$84+24=108$.

A composite solid made of prism A and prism B.

108 cubic units

Exercise 16 – Packing cubes

Box volume: $12\times9\times6=648$ cubic inches. One cube: $3\times3\times3=27$ cubic inches.

$648\div27=24$. Check by edges: $4\times3\times2=24$.

24 cubes

Exercise 17 – Filling a pool

Pool volume: $20\times10\times4=800$ cubic feet.

$\frac{3}{4}\times800=600$.

$600\text{ ft}^{3}$

Exercise 18 – Storage bin

Base area: $12\times6=72$.

$360\div72=5$.

Check: $72\times5=360$.

5 inches

Exercise 19 – Planter soil

First box: $6\times3\times2=36$. Second box: $3\times3\times1=9$.

Total: $36+9=45$ cubic feet.

Cost: $45\times4=180$ dollars.

A composite solid made of prism A and prism B.

$180

Exercise 20 – Cubes in a box

(a) $(10\div2)\times(8\div2)=5\times4=20$ cubes.

(b) $6\div2=3$ layers.

Check: each cube is $2\times2\times2=8$ cubic cm, and $60\times8=480=10\times8\times6$.

(a) 20; (b) 3; (c) 60 cubes

Key facts behind this volume practice solutions

Key facts

A unit cube has volume 1 cubic unit.
Volume is measured in cubic units such as cm³, in³ and ft³.
V = l × w × h, and V = B × h where B is the base area.
A composite solid made of two prisms has volume equal to the sum of the two volumes.
Volume = (cubes in one layer) × (number of layers).

How to use this volume practice solutions

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 practice solutions as a PDF with the button below and keep it with your notes.

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