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

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

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

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 $V=4\times4\times4=64$.

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

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

All Grade 5 chapters: Grade 5 math.

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

Exercise 1 – Count the cubes

Exercise 2 – Layers of cubes

Exercise 3 – Volume in cubic feet

Exercise 4 – Volume in cubic centimeters

Exercise 5 – Volume in cubic inches

Exercise 6 – Base area times height

Exercise 7 – Using the base area

Exercise 8 – Find the height

Exercise 9 – Find the missing edge

Exercise 10 – Volume of a cube

Exercise 11 – Prism from a picture

Exercise 12 – Fish tank

Exercise 13 – Compare two boxes

Exercise 14 – Two prisms joined

Exercise 15 – Step-shaped solid

Exercise 16 – Packing cubes

Exercise 17 – Filling a pool

Exercise 18 – Storage bin

Exercise 19 – Planter soil

Exercise 20 – Cubes in a box

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