5th Grade Math

5th Grade Math Quiz: Understand Volume As Cubic Units

Practice Understand Volume As Cubic Units in 5th Grade Math with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Understand Volume As Cubic Units, giving you a quick way to practice the rules, question types, and explanations that matter most for 5th Grade Math.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

Question 1

Ms. Rodriguez shows her class a box that can hold exactly 36 unit cubes when packed completely full. She fills it with unit cubes until it is $\frac{5}{6}$ full, then removes 8 unit cubes. What is the volume of the remaining unit cubes in the box?

20 cubic units
30 cubic units
28 cubic units
22 cubic units

Explanation: This problem tests your ability to work with fractions and perform multi-step calculations involving volume. When you see a question about filling containers with unit cubes, remember that volume equals the number of unit cubes that fit inside. Let's work through this step by step. The box holds exactly 36 unit cubes when completely full. First, find how many cubes are in the box when it's

\frac{5}{6}

full:

\frac{5}{6} \times 36 = 30

unit cubes. Then Ms. Rodriguez removes 8 cubes, so you subtract: unit cubes remaining. The volume is 22 cubic units.

Question 2

Tom built a tower using unit cubes in layers. Each layer has fewer cubes than the layer below it. The bottom layer has 9 unit cubes, the middle layer has 6 unit cubes, and the top layer has 3 unit cubes. If Tom adds one more layer on top with 2 unit cubes, what will be the volume of his complete tower?

324 cubic units because 9 × 6 × 3 × 2 = 324
18 cubic units because we only count the original three layers
20 cubic units because 9 + 6 + 3 + 2 = 20 unit cubes
22 cubic units because 9 + 6 + 3 + 2 + 2 extra = 22

Explanation: When you see a problem about finding the volume of a structure made from unit cubes, remember that volume measures how much space the entire structure occupies. Since each unit cube has a volume of 1 cubic unit, you need to count the total number of cubes in the whole tower. To find the total volume, you add up all the unit cubes in every layer: bottom layer (9 cubes) + middle layer (6 cubes) + top layer (3 cubes) + new top layer (2 cubes) =

unit cubes. Since each unit cube has a volume of 1 cubic unit, the total volume is 20 cubic units.

Question 3

Maya built a rectangular prism using unit cubes. She used 4 layers, and each layer had 6 unit cubes arranged in a 2 by 3 rectangle. Then she removed 3 unit cubes from the top layer to make a decoration. What is the volume of Maya's final solid figure?

21 cubic units
24 cubic units
18 cubic units
27 cubic units

Explanation: Maya started with 4 layers × 6 cubes per layer = 24 unit cubes. After removing 3 cubes from the top layer, she has 24 - 3 = 21 unit cubes remaining. Since volume equals the number of unit cubes that pack the figure, the volume is 21 cubic units. Choice B ignores the removal of cubes. Choice C miscalculates as 3 layers × 6 cubes. Choice D adds instead of subtracting the removed cubes.

Question 4

A storage box is packed completely full with unit cubes arranged in 3 layers. The bottom layer has 8 unit cubes, the middle layer has 6 unit cubes, and the top layer has 4 unit cubes. What is the volume of the storage box?

The volume is 8 cubic units because that's the largest layer
The volume is 18 cubic units because 8 + 6 + 4 = 18 unit cubes total
The volume is 192 cubic units because 8 × 6 × 4 = 192
The volume is 24 cubic units because 3 layers × 8 cubes = 24 cubes average

Explanation: Volume equals the total number of unit cubes that pack the figure. Adding all unit cubes: 8 + 6 + 4 = 18 unit cubes total, so volume is 18 cubic units. Choice A only counts the bottom layer. Choice C multiplies the layer sizes instead of adding them. Choice D incorrectly calculates an average using only the bottom layer size.

Question 5

Carlos has two identical cube-shaped containers. The first container can hold exactly 27 unit cubes when completely filled. If he fills the second container only $\frac{2}{3}$ full with unit cubes, what is the volume of the unit cubes in the second container?

18 cubic units
9 cubic units

Question 6

A solid is built from unit cubes (each cube is $1$ cubic unit). The cubes fill the space completely with no gaps or overlaps.

The solid has:

3 cubes on the bottom layer
3 cubes on the second layer stacked directly on the bottom layer
3 cubes on the third layer stacked directly on the second layer

Which statement about the volume is correct? (Volume is measured in cubic units.)

The volume is 9 cubic units because 9 unit cubes fill the solid with no gaps or overlaps.
The volume is 18 cubic units because each cube has 2 faces showing.
The volume is 3 cubic units because there are 3 layers.
The volume is 6 cubic units because you only count the cubes you can see from the front.

Explanation:

Question 7

A solid figure is built from unit cubes that fill the space completely with no gaps or overlaps. Volume is measured in cubic units.

The solid has 3 layers:

Layer 1 (bottom): 5 cubes in a straight row.
Layer 2 (middle): 5 cubes in a straight row stacked directly on top of Layer 1.
Layer 3 (top): 2 cubes stacked directly above the left end of the middle layer.

Which statement about the volume is correct?

The volume is 7 cubic units because you count only the cubes you can see from the front.
The volume is 12 cubic units because 12 unit cubes fill the solid with no gaps or overlaps.
The volume is 10 cubic units because the top layer does not change the volume.
The volume is 20 cubic units because you add the number of faces on the outside.

Explanation: Volume counts the number of cubic units that make up a solid figure. The unit cubes fill the space of the solid completely without any gaps or overlaps. Each unit cube adds one cubic unit to the total volume, so for this figure with 5 cubes in the bottom, 5 in the middle, and 2 on top, the total is 12 cubic units. To count the volume, add the number of cubes in each layer: 5 + 5 + 2 = 12. A common misconception is to count only visible cubes or ignore layers, but all cubes in every layer must be included. Cubic units measure the three-dimensional space occupied by any solid. This method allows us to calculate volume accurately for stacked or irregular shapes.

Question 8

A solid figure is built from unit cubes that fill the space completely with no gaps or overlaps. Volume is measured in cubic units.

The solid is made from 11 unit cubes. A student removes 2 cubes from the middle of the solid, leaving a hole (an empty space) inside.

Which statement about the volume is correct after the cubes are removed?

The volume is still 11 cubic units because the outside shape might look the same.
The volume is 9 cubic units because only 9 unit cubes are filling space now.
The volume is 13 cubic units because holes make the volume larger.
The volume cannot be found unless you count the outside faces of the solid.

Explanation: Volume counts the number of cubic units that make up a solid figure. The unit cubes fill the space of the solid completely without any gaps or overlaps. Each unit cube adds one cubic unit to the total volume, so after removing 2 cubes from 11, the remaining 9 cubes give a volume of 9 cubic units. To count the volume, subtract removed cubes from the original total: 11 - 2 = 9. A common misconception is that holes affect the volume differently, but volume is only the space filled by remaining cubes. Cubic units measure the three-dimensional space occupied by any solid. This method allows us to adjust volume calculations for changes like removals accurately.

Question 9

A solid is built from unit cubes that fill the space completely with no gaps or overlaps. Volume is measured in cubic units.

A student says, “This solid has a volume of 14 cubic units because I counted 14 cubes on the outside.”

But the solid is actually made of:

Bottom layer: 12 cubes arranged as a $4\times3$ rectangle.
Top layer: 4 cubes arranged as a $2\times2$ square stacked on one corner of the bottom layer.

Which statement about the student’s reasoning is correct?

The student is correct because volume is the number of cubes you can see.

Question 10

A student builds a solid from unit cubes (each cube is $1$ cubic unit). The cubes fill the space completely with no gaps or overlaps.

The student says, “The volume is the number of square units on the outside of the solid.”

Which statement is correct? (Volume is measured in cubic units.)

The student is correct because volume is the number of square units covering the outside.
The student is incorrect because volume is the total number of cubic units that fill the solid without gaps or overlaps.
The student is correct because volume counts the faces you can see.
The student is incorrect because volume only counts the bottom layer of cubes.

Explanation:

Question 11

A solid is built from unit cubes (each cube is $1$ cubic unit). The cubes fill the space completely with no gaps or overlaps.

Which statement about this solid’s volume is false? (Volume is measured in cubic units.)

The volume is the number of unit cubes that fill the solid with no gaps or overlaps.
Hidden cubes still count toward the volume because they fill space inside the solid.
If the solid is made from 11 unit cubes, then its volume is 11 cubic units.
The volume is found by counting only the cubes you can see on the outside of the solid.

Explanation: Volume counts the cubic units required to build or fill a solid. Filling without gaps means packing unit cubes completely, ensuring no overlaps or empty spaces remain. Each cube adds to the total volume, connecting the parts to the whole measurement. To count accurately, include every unit cube, even if hidden inside the solid. A misconception is that only visible cubes contribute to volume, but all cubes fill space. Cubic units allow for standardized volume assessment in three dimensions. This approach generalizes to measuring any solid's capacity effectively.

Question 12

A solid figure is built from unit cubes. The cubes fill the space completely with no gaps or overlaps. Volume is measured in cubic units.

The solid has 3 layers:

Bottom layer: 6 cubes arranged as a $3\times2$ rectangle.
Middle layer: 6 cubes arranged exactly the same on top of the bottom layer.
Top layer: 6 cubes arranged exactly the same on top of the middle layer.

Which statement about the volume is correct?

The volume is 6 cubic units because there are 6 cubes in one layer.
The volume is 12 cubic units because there are 2 layers you can see from the side.
The volume is 18 cubic units because 18 unit cubes fill the solid with no gaps or overlaps.

Question 13

A solid figure is built from unit cubes (each cube is $1$ cubic unit). The solid is a complete stack with no gaps or overlaps. It has 1 bottom layer of 10 cubes. On top, there is a second layer of 10 cubes placed directly above the bottom layer. A student says, “The volume is 20 square units because I counted 20 cubes.” Volume is measured in cubic units. Which statement is correct?

The student is correct because cubes can be counted in square units.
The volume is 20 cubic units because 20 unit cubes fill the solid without gaps or overlaps.
The volume is 10 cubic units because only one layer should be counted.
The volume is 40 cubic units because each cube has 2 layers of faces.

Explanation: Volume measures the amount of space a solid figure occupies by counting the number of cubic units it contains. In a complete stack, the unit cubes fill both layers without gaps or overlaps, ensuring all space is accounted for. Two layers each with 10 cubes connect to a total volume of 20 cubic units. Counting works by adding the cubes in each layer, using cubic units rather than square units. A misconception is labeling volume in square units, but volume requires cubic units to reflect three dimensions. Cubic units standardize the measurement of filled space in solids. This approach generalizes to calculating volumes by tallying unit cubes in any configuration.

Question 14

A solid figure is built from unit cubes (each cube is $1$ cubic unit). It is made of 3 layers. In each layer, there are 5 cubes arranged in a single row (so each layer has 5 cubes), and the layers are stacked directly on top of each other so the cubes fill the space without gaps or overlaps. Volume is measured in cubic units. Which statement about the volume is correct?

The volume is the number of unit cubes in the solid, because the cubes fill the space without gaps or overlaps.
The volume is the number of visible faces, because faces show how big the solid is.
The volume is the number of cubes on the outside only, because inside cubes do not count.
The volume is the number of squares on the surface, because volume is the same as surface area.

Explanation:

Question 15

Two solids are built from unit cubes (each cube is $1$ cubic unit). Solid A is a complete stack with 2 layers, and each layer has 6 cubes (the cubes fill the space without gaps or overlaps). Solid B is a complete stack with 3 layers, and each layer has 4 cubes (the cubes fill the space without gaps or overlaps). Volume is measured in cubic units. Which claim is correct?

Solid A has greater volume because it has more cubes in one layer.
Solid B has greater volume because it has more layers.
The two solids have the same volume because they each use 12 unit cubes to fill space.
The two solids have the same volume because they look different from the outside.

Explanation: Volume measures the amount of space a solid figure occupies by counting the number of cubic units it contains. The unit cubes in each solid must fill their respective spaces without gaps or overlaps for an accurate comparison of volumes. Solid A with 2 layers of 6 cubes each totals 12 cubic units, while Solid B with 3 layers of 4 cubes each also totals 12, showing equal volumes through the total cube count. Counting involves multiplying cubes per layer by the number of layers for each solid and comparing the results. A misconception is that more layers always mean greater volume, but it depends on the cubes per layer. Cubic units standardize volume measurement across different shapes and sizes. Ultimately, this method helps in understanding that rearranged cubes can maintain the same volume if the total count remains unchanged.

Question 16

A solid figure is built from unit cubes (each cube is $1$ cubic unit). It has 3 layers. The bottom layer has 4 cubes, the middle layer has 4 cubes stacked directly on top of them, and the top layer has 4 cubes stacked directly on top again. The cubes fill the space without gaps or overlaps. Volume is measured in cubic units. Which claim about cubic units is incorrect?

The volume is 12 cubic units because there are 12 unit cubes filling the solid.
If you remove 1 unit cube from the solid, the volume decreases by 1 cubic unit.
The volume is 6 cubic units because there are 6 faces on each cube.
Each unit cube counts as 1 cubic unit of volume.

Explanation: Volume measures the amount of space a solid figure occupies by counting the number of cubic units it contains. The stacked layers of unit cubes must fill the space without gaps or overlaps to represent the true volume. With 3 layers each of 4 cubes, the total of 12 cubic units directly connects to the number of cubes used. Counting involves summing all cubes across layers, not relating to the faces of individual cubes. A misconception is that volume relates to the 6 faces per cube, like claiming 6 cubic units for this figure, but volume counts whole cubes, not faces. Cubic units provide a foundational way to quantify three-dimensional space. This principle generalizes to measuring volumes of various objects by envisioning them filled with unit cubes.

Question 17

Two solids are built from unit cubes. In both solids, the cubes fill the space completely with no gaps or overlaps. Volume is measured in cubic units.

Solid A has 10 unit cubes. Solid B has 12 unit cubes.

Which statement about their volumes is correct?

Solid A has the greater volume because it might look taller.
Solid B has the greater volume because 12 unit cubes fill more space than 10 unit cubes.
Both solids have the same volume because they are made of unit cubes.
You cannot compare their volumes unless you count the outside faces.

Explanation: Volume counts the number of cubic units that make up a solid figure. The unit cubes fill the space of the solid completely without any gaps or overlaps. Each unit cube adds one cubic unit to the total volume, so Solid A with 10 cubes has 10 cubic units and Solid B with 12 has 12 cubic units, making B larger. To count the volume, simply total the number of unit cubes in each solid. A common misconception is that shape or height affects volume more than the total cubes, but it's solely the number of cubes that matters. Cubic units measure the three-dimensional space occupied by any solid. This method allows us to compare volumes of different figures accurately.

Question 18

Two solids are built from unit cubes (each cube is $1$ cubic unit). The cubes fill the space completely with no gaps or overlaps.

Solid A has 7 unit cubes. Solid B has 7 unit cubes.

Which statement about their volumes is correct? (Volume is measured in cubic units.)

Solid A has a greater volume because it might be taller.
Solid B has a greater volume because it might have more outside faces.
The solids have the same volume because each is filled by 7 unit cubes.
The solids could have different volumes even if they each use 7 unit cubes.

Explanation: Volume is the count of cubic units that occupy a solid's space. Filling without gaps means arranging unit cubes to fully pack the solid, avoiding any empty areas or overlaps. Each cube directly contributes to the total volume, so solids with the same number of cubes have equal volumes. Counting is simple: total the unit cubes used, like 7 for each solid. A misconception is that shape or height changes volume if cube count is the same, but volume depends only on the number of cubes. Cubic units provide a universal measure for volume in three-dimensional objects. This generalization applies to all shapes, ensuring fair comparisons.

Question 19

A solid figure is made from unit cubes (each cube is $1$ cubic unit). You can see the top is completely covered by a $3$ -by- $3$ array of cubes (9 cubes on top). The solid has 2 full layers stacked, and the cubes fill the space without gaps or overlaps. Volume is measured in cubic units. What is the volume of the solid?

9 cubic units
11 cubic units
18 cubic units

Question 20

Based on the cube structure shown, Kenji wants to build an identical structure right next to this one, sharing one complete face. How many unit cubes will be in both structures combined?

20 unit cubes because each structure has 10 cubes
16 unit cubes because they share 4 unit cubes on the touching face
14 unit cubes because 10 + 10 - 6 shared cubes
18 unit cubes because 10 + 10 - 2 cubes at the connection

Explanation: The original structure contains 10 unit cubes. Building an identical structure means adding another 10 unit cubes. Even though the structures share a face, each unit cube maintains its individual identity and volume. The total is 10 + 10 = 20 unit cubes. Choices B, C, and D incorrectly subtract cubes, misunderstanding that sharing faces doesn't reduce the count of individual unit cubes.

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5th Grade Math Quiz: Understand Volume As Cubic Units

What this quiz covers

How to use this quiz