5th Grade Volume of Rectangular Prisms Test Solutions and Scoring (PDF)

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

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This volume test answers 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.

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

Volume test answers: worked solutions

Question 1 – Counting unit cubes [2 pts]

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

Scoring: 1 point for each part.

Question 2 – Volume from edges [2 pts]

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

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

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

Question 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.

Question 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.

Question 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.

Question 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.

Question 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 – 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.

Question 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 volume test answers

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 test answers

Score your test with the point values shown for each question. Then read the worked solution of every question where you lost points and note the method to review.

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