5th Grade Volume of Rectangular Prisms Test Answer Key and Scoring Guide (PDF)

5th grade volume test answer key – Maths PDF

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This 5th grade volume test answer key 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.

Key takeaway: This answer key helps fifth grade students see how each point on the volume test was earned.

Topic: Volume of Rectangular Prisms (5th grade)
Content: Worked solutions and a scoring guide for 9 questions
Standards: 5.MD.C.3, 5.MD.C.4, 5.MD.C.5
Answers: Every step shown, with the method to review
Format: Free printable PDF, US Letter, black and white

This answer key helps fifth grade students see how each point on the volume test was earned. Also, it gives complete solutions to all nine questions, with the formula, the substitution, and the cubic units shown.

Question 4 finds a missing height, question 6 compares two packages, question 7 finds the volume of an aquarium, question 8 explains doubling edges, and question 9 counts stacked cubes. Add your points out of 20, then spend about 15 minutes redoing every question that lost credit. Then, draw each prism with labeled edges.

Use this key to score the test out of 20 points. Every answer shows the work and a scoring guide. Give partial credit when the setup is correct but one multiplication has a small slip.

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

5th grade volume test answer key: worked solutions

1 – Counting unit cubes [2 pts]

\(4\times3=12\) cubes
\(12\times2=24\) cubic units

Scoring: 1 point for each part.

2 – Volume from edges [2 pts]

\(V=9\times4\times3=108\).

\(108\text{ ft}^{3}\)

Also, Scoring: 1 point for a correct method, 1 point for 108 with cubic feet.

3 – Base area and height [2 pts]

\(V=B\times h=35\times6=210\).

\(210\text{ cm}^{3}\)

Scoring: 1 point for multiplying base area by height, 1 point for the answer with units.

4 – Missing height [2 pts]

Base area: \(8\times7=56\).

\(224\div56=4\).

4 in

Scoring: 1 point for the base area, 1 point for the height.

5 – Composite solid [3 pts]

\(6\times4\times3=72\) cubic units
\(3\times4\times1=12\) cubic units
\(72+12=84\) cubic units

A composite solid made of prism A and prism B.

Scoring: 1 point per part.

6 – Compare packages [2 pts]

Cereal: \(8\times2\times12=192\). Juice: \(5\times4\times10=200\).

The juice box is greater by \(8\text{ cm}^{3}\)

Scoring: 1 point for both volumes, 1 point for the comparison and difference.

7 – Aquarium [3 pts]

\(24\times12\times10=2{,}880\) cubic inches
\(24\times12\times8=2{,}304\) cubic inches
\(2{,}880-2{,}304=576\) cubic inches

Scoring: 1 point per part.

Question 8 and after

8 – Doubling edges [2 pts]

Original: \(2\times3\times4=24\). Double the height: \(2\times3\times8=48\), which is 2 times 24. Double all three edges: \(4\times6\times8=192\), which is 8 times 24.

Jamal is correct. Mei is not.

Scoring: 1 point for testing both ideas with numbers, 1 point for the correct conclusion.

9 – Stacked cubes [2 pts]

\(4\times5=20\) cubes per layer, so \(20\times3=60\text{ cm}^{3}\)
One more layer needs 20 cubes

A rectangular prism.

Scoring: 1 point for each part.

Total score

Total

20 points

Key facts behind this 5th grade volume test answer key

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.
Then, 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).

Common mistakes with this 5th grade volume test answer key

Students lose points for square units. Instead, write cubic units. Slow down at that step and check it twice.
Students skip the difference in question 6. Also, state which has more and by how much. Slow down at that step and check it twice.
Students forget the unit in question 9. Instead, the answer is in cubic centimeters. Slow down at that step and check it twice.
Students treat doubling as the same for all edges in question 8. Also, doubling all three edges gives eight times.

How to learn from your test

Sort lost points into formulas, missing edges, and stories. Practice the weakest group first. Repeat this habit on every problem for the best results.
Redo question 4 with a different volume. Also, new numbers show whether you understand division. Repeat this habit on every problem for the best results.
Teachers can ask students to explain a correction with layers of cubes. Repeat this habit on every problem for the best results.

Download the 5th grade volume test answer key as a PDF with the button below and keep it with your notes.

5th grade volume test answer key: frequently asked questions

What is the volume in question 2?

The prism is 9 feet long, 4 feet wide, and 3 feet high. So, multiplying gives 108 cubic feet. A quick check like this takes only a few seconds and prevents most errors. A quick check like this takes only a few seconds and prevents most errors.

How is the missing height found in question 4?

The base is 8 by 7, which is 56 square inches. Also, dividing the volume 224 by 56 gives a height of 4 inches. So, check that 8 times 7 times 4 is 224.

Who is right in question 8?

Jamal is right that doubling only the height doubles the volume. Also, Mei is right that doubling all three edges makes the volume eight times as large. Both statements can be true. A quick check like this takes only a few seconds and prevents most errors.

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