Elementary School Math Quiz: Find Volume Of Composite Figures

20 questions · exam conditions

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Find Volume Of Composite FiguresQuestion 1 of 20

A composite figure is made of two non-overlapping right rectangular prisms. Prism A is $6\text{ m} \times 2\text{ m} \times 2\text{ m}$ . Prism B is $6\text{ m} \times 1\text{ m} \times 2\text{ m}$ . The prisms touch but do not overlap, so total volume = volume of A + volume of B. What is the total volume?

24 cubic meters

36 cubic meters

42 cubic meters

60 cubic meters

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Elementary School Math Quiz

Elementary School Math Quiz: Find Volume Of Composite Figures

Practice Find Volume Of Composite Figures in Elementary School 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 Find Volume Of Composite Figures, giving you a quick way to practice the rules, question types, and explanations that matter most for Elementary School Math.

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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.

All questions

Question 1

24 cubic meters
36 cubic meters (correct answer)
42 cubic meters
60 cubic meters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the composite figure into its two non-overlapping right rectangular prisms, Prism A and Prism B. Calculate each part's volume using the formula length times width times height: Prism A is 6 m × 2 m × 2 m = 24 cubic meters, and Prism B is 6 m × 1 m × 2 m = 12 cubic meters. Add these volumes together to get the total: 24 + 12 = 36 cubic meters. A common misconception is to average the dimensions instead of calculating separately, but precise volumes require individual computations. In general, composite volumes are found by dividing into non-overlapping parts and summing their volumes. This fundamental concept is useful in fields like engineering for calculating material needs.

Question 2

A composite solid is made from two non-overlapping right rectangular prisms that meet along a face. Prism A is $9\text{ in} \times 2\text{ in} \times 2\text{ in}$ . Prism B is $1\text{ in} \times 2\text{ in} \times 2\text{ in}$ . The seam shows the parts do not overlap, so the total volume equals the sum of the parts: $V_{\text{total}}=V_A+V_B$ . What is the total volume?

36 cubic inches
40 cubic inches (correct answer)
72 cubic inches
80 cubic inches

Explanation: The core idea is that the volume of a composite figure is additive when it is made up of non-overlapping parts. To find the volume, we split the figure into two separate right rectangular prisms along the face where they meet. We calculate the volume of each prism by multiplying its length, width, and height; for Prism A, that's 9 in × 2 in × 2 in = 36 cubic in, and for Prism B, 1 in × 2 in × 2 in = 4 cubic in. Then, we add these volumes together to get the total volume: 36 + 4 = 40 cubic in. A common misconception is to subtract where the prisms join, thinking it removes duplicate volume, but since there's no overlap, subtraction is unnecessary. In general, composite volumes are found by decomposing the figure into simpler shapes like rectangular prisms. We then sum the volumes of these individual prisms to obtain the total volume, ensuring no overlaps.

Question 3

A baker stacks two rectangular cake blocks that touch but do not overlap (there is a clear boundary). Prism A measures 8 in by 2 in by 2 in. Prism B measures 4 in by 2 in by 2 in. The total volume equals the sum of the parts: $V_{total}=V_A+V_B$ . What is the total volume of the composite figure?

32 cubic inches
48 cubic inches (correct answer)
96 cubic inches
24 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of its parts. To find the volume of these stacked cake blocks, we split the composite figure into two right rectangular prisms that do not overlap. We calculate the volume of each prism by multiplying its length, width, and height: for Prism A, 8 in × 2 in × 2 in = 32 cubic inches, and for Prism B, 4 in × 2 in × 2 in = 16 cubic inches. Then, we add these volumes together: 32 + 16 = 48 cubic inches. A common misconception is that the way the prisms are joined might require subtracting volumes for overlaps, but since they do not overlap, we simply add without any subtraction. In general, to find the volume of any composite figure, we decompose it into familiar shapes like rectangular prisms. We then sum the volumes of these individual shapes to get the total volume.

Question 4

A toy block is made of two non-overlapping right rectangular prisms stacked like steps (they only touch, they do not overlap). Prism A is $8\text{ cm} \times 3\text{ cm} \times 2\text{ cm}$ . Prism B is $8\text{ cm} \times 3\text{ cm} \times 1\text{ cm}$ . The total volume equals the sum of the volumes of Prism A and Prism B. What is the total volume of the toy block?

48 cubic centimeters
72 cubic centimeters (correct answer)
96 cubic centimeters
120 cubic centimeters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the toy block into its two non-overlapping right rectangular prisms, Prism A and Prism B, stacked like steps. Calculate each part's volume using the formula length times width times height: Prism A is 8 cm × 3 cm × 2 cm = 48 cubic centimeters, and Prism B is 8 cm × 3 cm × 1 cm = 24 cubic centimeters. Add these volumes together to get the total: 48 + 24 = 72 cubic centimeters. A common misconception is to multiply dimensions of the whole figure instead of parts, but splitting ensures accurate individual volumes. In general, composite volumes are found by dividing the shape into non-overlapping prisms and adding their volumes. This principle extends to more complex figures, promoting a systematic way to compute total space.

Question 5

A storage box is made by joining two non-overlapping right rectangular prisms. Prism A is $6\text{ in} \times 4\text{ in} \times 3\text{ in}$ . Prism B is $6\text{ in} \times 2\text{ in} \times 3\text{ in}$ . The prisms touch along a face, so there is no overlap. The total volume equals the sum of the volumes of Prism A and Prism B. What is the total volume of the composite figure?

72 cubic inches
108 cubic inches (correct answer)
180 cubic inches
216 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the composite storage box into its two non-overlapping right rectangular prisms, Prism A and Prism B. Calculate each part's volume using the formula length times width times height: Prism A is 6 in × 4 in × 3 in = 72 cubic inches, and Prism B is 6 in × 2 in × 3 in = 36 cubic inches. Add these volumes together to get the total: 72 + 36 = 108 cubic inches. A common misconception is to subtract volumes if prisms touch, but since they don't overlap, you simply add without subtracting. In general, composite volumes are found by decomposing the figure into simpler shapes like prisms and ensuring no overlap in the parts. This method applies to any composite solid made of non-overlapping rectangular prisms, making volume calculation straightforward and accurate.

Question 6

A classroom supply organizer is a composite solid made from two non-overlapping right rectangular prisms. Prism A measures $7\text{ in} \times 3\text{ in} \times 2\text{ in}$ . Prism B measures $7\text{ in} \times 3\text{ in} \times 1\text{ in}$ . The prisms touch along a face, so volume is additive: total volume = volume of A + volume of B. What is the total volume?

42 cubic inches
84 cubic inches
63 cubic inches (correct answer)
126 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the classroom supply organizer into its two non-overlapping right rectangular prisms, Prism A and Prism B. Calculate each part's volume using the formula length times width times height: Prism A is 7 in × 3 in × 2 in = 42 cubic inches, and Prism B is 7 in × 3 in × 1 in = 21 cubic inches. Add these volumes together to get the total: 42 + 21 = 63 cubic inches. A common misconception is that shared faces mean subtracting area, but volume addition ignores contact if no overlap occurs. In general, composite volumes are found by decomposing into simpler rectangular prisms and summing them up. This method is versatile for real-world objects, like furniture or buildings, composed of multiple parts.

Question 7

A composite solid is built from two non-overlapping right rectangular prisms with a seam showing the split. Prism A is $4\text{ ft} \times 4\text{ ft} \times 2\text{ ft}$ . Prism B is $4\text{ ft} \times 1\text{ ft} \times 2\text{ ft}$ . Since the parts do not overlap, the total volume equals the sum of the parts: $V_{\text{total}}=V_A+V_B$ . What is the total volume?

32 cubic feet
40 cubic feet (correct answer)
48 cubic feet
80 cubic feet

Explanation: The core idea is that the volume of a composite figure is additive when it is made up of non-overlapping parts. To find the volume, we split the figure into two separate right rectangular prisms along the seam showing the split. We calculate the volume of each prism by multiplying its length, width, and height; for Prism A, that's 4 ft × 4 ft × 2 ft = 32 cubic ft, and for Prism B, 4 ft × 1 ft × 2 ft = 8 cubic ft. Then, we add these volumes together to get the total volume: 32 + 8 = 40 cubic ft. A common misconception is to use only the largest dimensions for the whole figure, but that ignores the composite nature and gives an wrong volume. In general, composite volumes are found by decomposing the figure into simpler shapes like rectangular prisms. We then sum the volumes of these individual prisms to obtain the total volume, ensuring no overlaps.

Question 8

A classroom display stand is built from two non-overlapping right rectangular prisms with a clear boundary between them. Prism A is $7\text{ ft} \times 2\text{ ft} \times 1\text{ ft}$ . Prism B is $3\text{ ft} \times 2\text{ ft} \times 1\text{ ft}$ . Because they do not overlap, the total volume equals the sum of the parts: $V_{\text{total}}=V_A+V_B$ . What is the total volume of the stand?

14 cubic feet
20 cubic feet (correct answer)
40 cubic feet
84 cubic feet

Explanation: The core idea is that the volume of a composite figure is additive when it is made up of non-overlapping parts. To find the volume, we split the figure into two separate right rectangular prisms along the clear boundary where they touch. We calculate the volume of each prism by multiplying its length, width, and height; for Prism A, that's 7 ft × 2 ft × 1 ft = 14 cubic ft, and for Prism B, 3 ft × 2 ft × 1 ft = 6 cubic ft. Then, we add these volumes together to get the total volume: 14 + 6 = 20 cubic ft. A common misconception is to think overlapping occurs at the boundary, but since they only touch on a face with no shared volume, addition is direct. In general, composite volumes are found by decomposing the figure into simpler shapes like rectangular prisms. We then sum the volumes of these individual prisms to obtain the total volume, ensuring no overlaps.

Question 9

32 cubic inches
48 cubic inches (correct answer)
96 cubic inches
24 cubic inches

Question 10

A swimming pool consists of a shallow end and a deep end, both shaped like rectangular prisms. The shallow end measures $20$ feet by $15$ feet by $4$ feet deep. The deep end measures $20$ feet by $10$ feet by $8$ feet deep. If it costs $3.50 to heat each $ $100$ $ cubic feet of water, how much does it cost to heat the entire pool?

$98.00 (correct answer)
$105.00
$91.00
$112.00

Explanation: Shallow end volume:

20 \times 15 \times 4 = 1,200

cubic feet. Deep end volume:

20 \times 10 \times 8 = 1,600

cubic feet. Total volume:

1,200 + 1,600 = 2,800

cubic feet. Number of 100-cubic-foot units:

2,800 \div 100 = 28

units. Total cost:

28 \times \$3.50 = \$98.00

. Choice B represents using 30 units instead of 28. Choice C represents using 26 units. Choice D represents using 32 units, possibly from calculation errors in the individual volumes.

Question 11

A small aquarium stand is made from two right rectangular prisms placed together without overlapping, and the boundary between them is marked. Prism A measures 5 in by 5 in by 2 in. Prism B measures 1 in by 5 in by 2 in. The total volume equals the sum of the parts: $V_{total}=V_A+V_B$ . What is the total volume of the composite figure?

50 cubic inches
60 cubic inches (correct answer)
75 cubic inches
12 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of its parts. To find the volume of this aquarium stand, we split the composite figure into two right rectangular prisms that do not overlap. We calculate the volume of each prism by multiplying its length, width, and height: for Prism A, 5 in × 5 in × 2 in = 50 cubic inches, and for Prism B, 1 in × 5 in × 2 in = 10 cubic inches. Then, we add these volumes together: 50 + 10 = 60 cubic inches. A common misconception is that the way the prisms are joined might require subtracting volumes for overlaps, but since they do not overlap, we simply add without any subtraction. In general, to find the volume of any composite figure, we decompose it into familiar shapes like rectangular prisms. We then sum the volumes of these individual shapes to get the total volume.

Question 12

A ramp display is built from two non-overlapping right rectangular prisms. Prism A measures $9\text{ in} \times 2\text{ in} \times 2\text{ in}$ . Prism B measures $9\text{ in} \times 2\text{ in} \times 1\text{ in}$ . The prisms touch along a face, so the total volume equals the sum of their volumes. What is the total volume?

18 cubic inches
27 cubic inches
54 cubic inches (correct answer)
72 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the ramp display into its two non-overlapping right rectangular prisms, Prism A and Prism B. Calculate each part's volume using the formula length times width times height: Prism A is 9 in × 2 in × 2 in = 36 cubic inches, and Prism B is 9 in × 2 in × 1 in = 18 cubic inches. Add these volumes together to get the total: 36 + 18 = 54 cubic inches. A common misconception is that the total volume is just the larger prism's, ignoring the smaller one, but both must be included. In general, composite volumes are found by breaking the figure into prisms and adding their individual volumes. This process helps in understanding how to measure irregular shapes by simplifying them into familiar forms.

Question 13

A classroom display is built from two non-overlapping right rectangular prisms, separated by a clear edge. Prism A is 4 m by 3 m by 2 m. Prism B is 1 m by 3 m by 2 m. The total volume equals the sum of the parts: $V_{total}=V_A+V_B$ . What is the total volume of the composite figure?

24 cubic meters
30 cubic meters (correct answer)
60 cubic meters
15 cubic meters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of its parts. To find the volume of this classroom display, we split the composite figure into two right rectangular prisms that do not overlap. We calculate the volume of each prism by multiplying its length, width, and height: for Prism A, 4 m × 3 m × 2 m = 24 cubic meters, and for Prism B, 1 m × 3 m × 2 m = 6 cubic meters. Then, we add these volumes together: 24 + 6 = 30 cubic meters. A common misconception is that the way the prisms are joined might require subtracting volumes for overlaps, but since they do not overlap, we simply add without any subtraction. In general, to find the volume of any composite figure, we decompose it into familiar shapes like rectangular prisms. We then sum the volumes of these individual shapes to get the total volume.

Question 14

A student says, "To find the volume of this composite solid, I can add the volumes of the two prisms because they do not overlap." The solid is made from two non-overlapping right rectangular prisms: Prism A is $10\text{ in} \times 2\text{ in} \times 1\text{ in}$ and Prism B is $10\text{ in} \times 2\text{ in} \times 2\text{ in}$ . The total volume equals the sum of the parts. What is the total volume of the composite solid?

20 cubic inches
40 cubic inches
60 cubic inches (correct answer)
80 cubic inches

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the composite solid into its two non-overlapping right rectangular prisms, Prism A and Prism B, as the student described. Calculate each part's volume using the formula length times width times height: Prism A is 10 in × 2 in × 1 in = 20 cubic inches, and Prism B is 10 in × 2 in × 2 in = 40 cubic inches. Add these volumes together to get the total: 20 + 40 = 60 cubic inches. A common misconception is to use the overall dimensions without splitting, which might overestimate or underestimate. In general, composite volumes are found by identifying separate prisms and summing their volumes accurately. This method builds a strong foundation for handling more intricate 3D shapes in mathematics.

Question 15

A composite solid is made from two non-overlapping right rectangular prisms that share the same height. Prism A is $4\text{ ft} \times 2\text{ ft} \times 3\text{ ft}$ . Prism B is $2\text{ ft} \times 2\text{ ft} \times 3\text{ ft}$ . They touch along a face (no overlap). The total volume equals the sum of the parts. What is the total volume of the composite solid?

24 cubic feet
36 cubic feet (correct answer)
48 cubic feet
72 cubic feet

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the composite solid into its two non-overlapping right rectangular prisms, Prism A and Prism B, sharing the same height. Calculate each part's volume using the formula length times width times height: Prism A is 4 ft × 2 ft × 3 ft = 24 cubic feet, and Prism B is 2 ft × 2 ft × 3 ft = 12 cubic feet. Add these volumes together to get the total: 24 + 12 = 36 cubic feet. A common misconception is to add only unique dimensions, but each prism's full volume must be calculated separately. In general, composite volumes are found by identifying and summing the volumes of non-overlapping components. This technique applies broadly to architecture and design, where structures are built from multiple blocks.

Question 16

24 cubic meters
30 cubic meters (correct answer)
60 cubic meters
15 cubic meters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of its parts. To find the volume of this classroom display, we split the composite figure into two right rectangular prisms that do not overlap. We calculate the volume of each prism by multiplying its length, width, and height: for Prism A, 4 m × 3 m × 2 m = 24 cubic meters, and for Prism B, 1 m × 3 m × 2 m = 6 cubic meters. Then, we add these volumes together: 24 + 6 = 30 cubic meters. A common misconception is that the way the prisms are joined might require subtracting volumes for overlaps, but since they do not overlap, we simply add without any subtraction. In general, to find the volume of any composite figure, we decompose it into familiar shapes like rectangular prisms. We then sum the volumes of these individual shapes to get the total volume.

Question 17

A toy is made by attaching two non-overlapping right rectangular prisms side by side. Prism A is $8\text{ cm} \times 2\text{ cm} \times 2\text{ cm}$ . Prism B is $3\text{ cm} \times 2\text{ cm} \times 2\text{ cm}$ . The seam shows the parts do not overlap, so the total volume equals the sum of the parts: $V_{\text{total}}=V_A+V_B$ . What is the total volume?

32 cubic centimeters
44 cubic centimeters (correct answer)
88 cubic centimeters
176 cubic centimeters

Explanation: The core idea is that the volume of a composite figure is additive when it is made up of non-overlapping parts. To find the volume, we split the figure into two separate right rectangular prisms side by side along the attachment point. We calculate the volume of each prism by multiplying its length, width, and height; for Prism A, that's 8 cm × 2 cm × 2 cm = 32 cubic cm, and for Prism B, 3 cm × 2 cm × 2 cm = 12 cubic cm. Then, we add these volumes together to get the total volume: 32 + 12 = 44 cubic cm. A common misconception is to add the surface areas instead of volumes, but volume measures the space inside, so we use the product of three dimensions for each part. In general, composite volumes are found by decomposing the figure into simpler shapes like rectangular prisms. We then sum the volumes of these individual prisms to obtain the total volume, ensuring no overlaps.

Question 18

A cafeteria makes a block display from two non-overlapping right rectangular prisms. Prism A is $10\text{ cm} \times 3\text{ cm} \times 1\text{ cm}$ . Prism B is $10\text{ cm} \times 3\text{ cm} \times 2\text{ cm}$ . The boundary between them is clear, so the total volume equals the sum of the parts: $V_{\text{total}}=V_A+V_B$ . What is the total volume of the composite figure?

30 cubic centimeters
60 cubic centimeters
90 cubic centimeters (correct answer)
180 cubic centimeters

Explanation: The core idea is that the volume of a composite figure is additive when it is made up of non-overlapping parts. To find the volume, we split the figure into two separate right rectangular prisms along the clear boundary. We calculate the volume of each prism by multiplying its length, width, and height; for Prism A, that's 10 cm × 3 cm × 1 cm = 30 cubic cm, and for Prism B, 10 cm × 3 cm × 2 cm = 60 cubic cm. Then, we add these volumes together to get the total volume: 30 + 60 = 90 cubic cm. A common misconception is to average the dimensions instead of adding volumes, but that doesn't account for the actual space occupied. In general, composite volumes are found by decomposing the figure into simpler shapes like rectangular prisms. We then sum the volumes of these individual prisms to obtain the total volume, ensuring no overlaps.

Question 19

A science class makes a step-shaped block from two right rectangular prisms placed side-by-side with a clear seam between them (no overlap). Prism A is 5 cm by 3 cm by 4 cm. Prism B is 2 cm by 3 cm by 4 cm. The total volume equals the sum of the parts: $V_{total}=V_A+V_B$ . What is the total volume of the composite figure?

60 cubic centimeters
84 cubic centimeters (correct answer)
20 cubic centimeters
140 cubic centimeters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of its parts. To find the volume of this step-shaped block, we split the composite figure into two right rectangular prisms that do not overlap. We calculate the volume of each prism by multiplying its length, width, and height: for Prism A, 5 cm × 3 cm × 4 cm = 60 cubic centimeters, and for Prism B, 2 cm × 3 cm × 4 cm = 24 cubic centimeters. Then, we add these volumes together: 60 + 24 = 84 cubic centimeters. A common misconception is that the way the prisms are joined might require subtracting volumes for overlaps, but since they do not overlap, we simply add without any subtraction. In general, to find the volume of any composite figure, we decompose it into familiar shapes like rectangular prisms. We then sum the volumes of these individual shapes to get the total volume.

Question 20

A composite solid is built from two non-overlapping right rectangular prisms that fit together like an L-shape (they touch along a face). Prism A measures $5\text{ cm} \times 5\text{ cm} \times 2\text{ cm}$ . Prism B measures $5\text{ cm} \times 2\text{ cm} \times 2\text{ cm}$ . The total volume equals the sum of the volumes of the two prisms. What is the total volume?

50 cubic centimeters
70 cubic centimeters (correct answer)
90 cubic centimeters
140 cubic centimeters

Explanation: The core idea when finding the volume of composite figures is that volume is additive, meaning the total volume is the sum of the volumes of the individual parts as long as they don't overlap. To solve this, split the L-shaped composite solid into its two non-overlapping right rectangular prisms, Prism A and Prism B. Calculate each part's volume using the formula length times width times height: Prism A is 5 cm × 5 cm × 2 cm = 50 cubic centimeters, and Prism B is 5 cm × 2 cm × 2 cm = 20 cubic centimeters. Add these volumes together to get the total: 50 + 20 = 70 cubic centimeters. A common misconception is that the L-shape requires subtracting overlap, but since they only touch, no subtraction is needed. In general, composite volumes are found by decomposing into basic shapes and adding their volumes. This strategy simplifies complex figures, making volume accessible for students.