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Quizzes > High School Quizzes > Mathematics

Rectangular Prism Volume Practice Quiz

Sharpen skills with composite and prism volume exercises

Difficulty: Moderate
Grade: Grade 6
Study OutcomesCheat Sheet
Colorful paper art promoting The Composite Prism Challenge, a geometry trivia for high school students.

What is the formula to calculate the volume of a rectangular prism?
Length × Width × Height
Length + Width + Height
2(Length + Width + Height)
Length × Width × 2
The volume of a rectangular prism is computed by multiplying its length, width, and height. This product gives you the total space inside the prism.
A rectangular prism has a length of 5 cm, a width of 3 cm, and a height of 2 cm. What is its volume?
10 cm³
15 cm³
30 cm³
60 cm³
Multiply the dimensions: 5 × 3 × 2 = 30 cm³. Therefore, the correct volume is 30 cubic centimeters.
Which of the following is the most appropriate unit for measuring volume?
Meters
Square Meters
Cubic Centimeters
Centimeters
Volume is measured in cubic units because it represents three-dimensional space. Thus, cubic centimeters is the correct unit choice.
If you double each dimension of a rectangular prism, by what factor does the volume increase?
8
2
6
4
Doubling each dimension multiplies the volume by 2 × 2 × 2, which equals 8. This shows that the volume increases eightfold.
What is the surface area of a rectangular prism with dimensions length = 4 cm, width = 3 cm, and height = 2 cm?
52 cm²
48 cm²
26 cm²
24 cm²
Using the surface area formula: 2(lw + lh + wh) = 2(12 + 8 + 6) = 2(26) = 52 cm². Therefore, the correct answer is 52 cm².
A composite solid consists of a rectangular prism with a cube attached to one of its faces. If the rectangular prism has a volume of 60 cm³ and the cube has a volume of 8 cm³, what is the total volume?
68 cm³
70 cm³
62 cm³
80 cm³
The total volume is the sum of the volumes of the rectangular prism and the cube: 60 cm³ + 8 cm³ = 68 cm³. Therefore, the correct answer is 68 cm³.
Given a rectangular prism with dimensions 7 m, 4 m, and 3 m, what is its surface area?
84 m²
122 m²
130 m²
96 m²
The surface area is calculated as 2(7×4 + 7×3 + 4×3) = 2(28 + 21 + 12) = 2(61) = 122 m². Option B is correct.
A composite shape is made of two rectangular prisms joined along a face. Prism A has dimensions 4 cm, 6 cm, and 3 cm, and Prism B has dimensions 4 cm, 6 cm, and 2 cm. What is the combined volume?
120 cm³
110 cm³
96 cm³
128 cm³
Volume of Prism A is 4×6×3 = 72 cm³ and Prism B is 4×6×2 = 48 cm³. Their sum is 72 + 48 = 120 cm³, which is the correct answer.
If you know the volume of a rectangular prism and two of its dimensions, which formula can be used to find the third dimension?
Third dimension = (Length + Width) / Volume
Third dimension = Volume / (Length × Width)
Third dimension = (Length × Width) / Volume
Third dimension = Volume / (Length + Width)
By rearranging the formula Volume = Length × Width × Height, the unknown dimension (Height) is given by Volume divided by (Length × Width). Option B is correct.
A composite shape has a rectangular prism with a triangular prism removed from it. If the rectangular prism has a volume of 150 cm³ and the triangular prism removed has a volume of 50 cm³, what is the remaining volume?
100 cm³
120 cm³
90 cm³
50 cm³
Subtract the volume of the removed triangular prism from the volume of the rectangular prism: 150 cm³ - 50 cm³ = 100 cm³. Therefore, the correct answer is 100 cm³.
A composite solid consists of a cylinder attached to the top of a rectangular prism. Which of the following is true when calculating the total volume?
Calculate the volume of the prism and the cylinder separately, then add them
Multiply the volumes of both shapes
Only calculate the volume of the larger shape
Add the surface areas instead of volumes
For composite solids, calculate the volume of each individual part separately and then add them together. This method yields the total volume.
A rectangular prism has a volume of 200 cm³ and a base area of 20 cm². What is its height?
5 cm
10 cm
15 cm
20 cm
The height can be found by dividing the volume by the base area: 200 cm³ / 20 cm² = 10 cm. Thus, option B is correct.
What effect does multiplying each dimension of a rectangular prism by a factor of k have on its volume?
Volume is multiplied by k
Volume is multiplied by k²
Volume is multiplied by k³
Volume is multiplied by 3k
When each dimension is multiplied by k, the volume is multiplied by k three times (one for each dimension), resulting in a multiplication factor of k³. Therefore, option C is correct.
If the length of a rectangular prism is increased by 50% while the width and height remain unchanged, by what factor does the volume increase?
1.25 times
1.5 times
2 times
3 times
Only one dimension (the length) increases by 50%, so the new volume becomes 1.5 times the original volume, while the other dimensions remain constant. This makes option B the correct answer.
A composite shape is formed by joining a triangular prism and a rectangular prism along one of their rectangular faces. Which method is best for finding its total volume?
Multiply the volumes of both prisms
Divide the sum of the volumes by two
Add the individual volumes
Subtract the triangular prism's volume from the rectangular prism
For composite shapes, the total volume is obtained by adding the volumes of the individual parts. Option C is the correct method.
A rectangular prism has a surface area of 94 cm² and dimensions 3 cm, 4 cm, and h cm. What is the value of h?
4 cm
5 cm
6 cm
7 cm
Using the surface area formula 2(3×4 + 3×h + 4×h) = 94 simplifies to 24 + 14h = 94. Solving 14h = 70 gives h = 5 cm, so option B is correct.
When combining two solids to form a composite figure, under what condition should you subtract a volume?
Always add the volumes
Subtract a volume if one shape is nested inside the other
Subtract any volume if the shapes touch
Multiply the overlapping region by a factor
Subtraction is applied when one solid overlaps or is removed from another. This typically occurs when one shape is nested within another, making option B correct.
A composite object is made of a cube and a rectangular prism attached at one face. The cube has an edge length of 3 cm, and the rectangular prism has dimensions 3 cm × 3 cm × 5 cm. What is the total surface area of the composite object, considering the attached face is not exposed?
130 cm²
114 cm²
108 cm²
96 cm²
The cube has a surface area of 54 cm² and the prism 78 cm². Since the two share a face of area 9 cm², subtracting twice this area (18 cm²) from the sum gives 54 + 78 - 18 = 114 cm². Option B is correct.
Which of the following best describes a composite shape?
A shape that can be divided into two or more simple geometric figures
A shape with curved surfaces only
A shape that has no volume
A shape with only identical faces
A composite shape is one that can be broken down into simpler, basic geometric figures such as rectangles, triangles, or circles. This property makes option A correct.
If the volume of a composite shape is the sum of the volumes of its parts, which mathematical operation is used?
Addition
Subtraction
Multiplication
Division
The correct procedure for finding the total volume of a composite shape is to add the volumes of the individual parts together. This makes addition the appropriate operation.
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Study Outcomes

  1. Analyze composite shapes to identify individual components.
  2. Apply volume formulas to solve problems involving rectangular prisms.
  3. Calculate the surface area of composite structures with precision.
  4. Synthesize geometric concepts to evaluate overall structure dimensions.
  5. Verify problem solutions using systematic reasoning and formula application.

Volume of Rectangular Prism Worksheet Cheat Sheet

  1. Visualize Composite Prisms - Think of composite prisms as Lego blocks built from simpler prisms. By picturing how each piece fits together, you can split the solid into familiar shapes and tackle each section step by step. This strategy makes even the trickiest solids feel manageable. Composite Figures Guide by Byju's
  2. Master Rectangular Prism Volume - Remember that every rectangular prism's volume equals length × width × height. Once you're comfortable with this formula, you can apply it to each block in your composite figure. It's the cornerstone of all volume calculations! Volume of Rectangular Prisms on Byju's
  3. Sum Up Surface Areas - To find the total surface area of a composite solid, calculate the area of each face and then add them all together. Don't forget to subtract any overlapping or hidden faces so you don't double-count. This method ensures your surface area is spot-on. Surface Area of Composite Figures
  4. Decompose Complex Shapes - When a shape looks intimidating, break it down into basic prisms like cubes, rectangular boxes, or wedges. Solving each piece on its own is much easier than tackling the monster shape head-on. Practice this habit and you'll breeze through problems! Decomposing with Byju's
  5. Know Other Shapes' Formulas - Composite solids sometimes hide cylinders, cones, or spheres inside them. Familiarize yourself with each formula so you can spot these shapes immediately and calculate their volumes with confidence. The more formulas you know, the more tools you have in your math toolbox! Volume of Composite Solids Worksheet
  6. Use the Additive Volume Principle - The total volume of a composite solid is just the sum of its non‑overlapping parts. Calculate each piece separately, then add them up for a swift and accurate result. It's like collecting puzzle pieces - you get the full picture by merging each volume. Composite Solid Volume Method
  7. Check Your Units - Always confirm that length, width, height, and any radii are all in the same unit before calculating. Mixing centimeters with meters or inches throws off your final answer. Consistent units keep your results precise and error‑free. Composite Prism Worksheet
  8. Tackle Real‑World Problems - Apply your skills to real‑life situations like packaging design or aquarium building to see concepts in action. Working on tangible scenarios cements your understanding and makes math more engaging. Plus, it's fun to solve problems you can actually visualize! Practical Composite Solids Quiz
  9. Review Worked Examples - Study step‑by‑step solutions to discover common tricks, shortcuts, and pitfalls. Analyzing solved problems boosts your confidence and shows you how experts approach each challenge. It's like having a personal tutor guiding you through every calculation. Composite Solids Worked Examples
  10. Quiz Yourself with Interactive Worksheets - Test your knowledge with online exercises and timed drills to pinpoint areas that need extra practice. Interactive tools give instant feedback so you can correct mistakes on the spot. Regular quizzes transform you from a novice into a composite‑prism pro! Interactive Volume Worksheets
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