Unlock hundreds more features
Save your Quiz to the Dashboard
View and Export Results
Use AI to Create Quizzes and Analyse Results

OR
Sign inSign in with Facebook
Sign inSign in with Google
Quizzes > High School Quizzes > Mathematics

Additive Volume Practice Quiz Worksheets

Enhance your volume mastery through engaging quizzes

Difficulty: Moderate
Grade: Grade 4
Study OutcomesCheat Sheet
Colorful paper art promoting a dynamic math quiz on additive volume for middle school students.

A small box has a volume of 24 cubic units and a larger box has a volume of 36 cubic units. What is the total volume of the two boxes?
60 cubic units
72 cubic units
84 cubic units
96 cubic units
The total volume is found by simply adding the two volumes: 24 + 36 = 60 cubic units. This basic addition reinforces the concept of additive volume.
A cube has a side length of 3 units. What is the volume of the cube?
27 cubic units
9 cubic units
18 cubic units
81 cubic units
The volume of a cube is calculated using the formula side³. Here, 3³ equals 27 cubic units. This question helps students practice power operations and volume calculations.
A rectangular box has dimensions 4 units by 3 units by 2 units. What is its volume?
24 cubic units
18 cubic units
20 cubic units
30 cubic units
The volume of a rectangular prism is the product of its length, width, and height: 4 × 3 × 2 = 24 cubic units. This problem reinforces the basic volume formula for prisms.
Two identical rectangular prisms, each with a volume of 15 cubic units, are combined. What is the total volume?
30 cubic units
15 cubic units
60 cubic units
45 cubic units
Since the two prisms are identical with each having 15 cubic units, their combined volume is 15 + 15 = 30 cubic units. This straightforward addition highlights the additive nature of volume.
If a rectangular container has a volume of 40 cubic units and an additional box of 10 cubic units is added, what is the new total volume?
50 cubic units
40 cubic units
60 cubic units
70 cubic units
The total volume is the sum of the individual volumes: 40 + 10 equals 50 cubic units. This question emphasizes the simple addition of volumes.
A composite shape consists of a rectangular prism with dimensions 4 units by 3 units by 2 units and a cube with a side length of 2 units attached to one face. What is the total volume of the composite shape?
32 cubic units
30 cubic units
34 cubic units
40 cubic units
First, calculate the volume of the rectangular prism: 4 × 3 × 2 = 24 cubic units. Next, compute the cube's volume: 2³ = 8 cubic units. Adding them gives a total of 24 + 8 = 32 cubic units.
A cylindrical can has a volume of 150 cubic centimeters. If a cone with the same base and height as the cylinder is removed from the can, what is the volume of the removed cone?
50 cubic centimeters
75 cubic centimeters
100 cubic centimeters
150 cubic centimeters
The volume of a cone is one third the volume of a cylinder with the same dimensions. Therefore, 1/3 of 150 cubic centimeters is 50 cubic centimeters. This question demonstrates the relationship between the volumes of cones and cylinders.
You have three cubes with side lengths of 2 units, 3 units, and 4 units respectively. What is the sum of their volumes?
99 cubic units
91 cubic units
108 cubic units
110 cubic units
Calculate each cube's volume using side³: 2³ = 8, 3³ = 27, and 4³ = 64. Adding these gives 8 + 27 + 64 = 99 cubic units. This reinforces the concept of volume calculation for cubes.
A swimming pool is designed as a rectangular prism with dimensions 10 m × 5 m × 2 m and has a half-cylinder attached along its length with a radius of 2.5 m. What is the approximate total volume of the pool?
Approximately 198 cubic meters
Approximately 188 cubic meters
Approximately 209 cubic meters
Approximately 210 cubic meters
The volume of the rectangular prism is 10 × 5 × 2 = 100 m³. The full cylinder would have a volume of π × (2.5)² × 10 ≈ 62.5π m³, so half of that is about 31.25π ≈ 98 m³. Added together, the total is roughly 100 + 98 = 198 m³.
A storage container is created by attaching a cube with a side length of 3 units to a rectangular prism with dimensions 3 units, 4 units, and 2 units. What is the total volume of the container?
51 cubic units
54 cubic units
48 cubic units
60 cubic units
The cube's volume is 3³ = 27 cubic units and the rectangular prism's volume is 3 × 4 × 2 = 24 cubic units. Their sum, 27 + 24, equals 51 cubic units.
A composite figure is made up of two parts: one rectangular prism with a volume of 20 cubic units and another rectangular prism with dimensions 2 units, 5 units, and 3 units. What is the total volume of the figure?
50 cubic units
20 cubic units
30 cubic units
60 cubic units
First, calculate the volume of the second prism: 2 × 5 × 3 = 30 cubic units. Adding the first volume of 20 cubic units gives a total of 20 + 30 = 50 cubic units.
Two cylinders are placed side by side. Cylinder A has a volume of 100π cubic centimeters and Cylinder B has a volume of 150π cubic centimeters. What is the combined volume of the two cylinders expressed in terms of π?
250π cubic centimeters
300π cubic centimeters
200π cubic centimeters
150π cubic centimeters
Simply add the two volumes: 100π + 150π = 250π cubic centimeters. This problem applies the additive property of volume to circular solids.
A water tank consists of a rectangular prism with dimensions 8 m × 3 m × 2 m and a triangular prism attached on top, where the area of the triangular base is 6 m² and the length is 8 m. What is the overall volume of the tank?
96 cubic meters
88 cubic meters
104 cubic meters
112 cubic meters
The rectangular prism volume is 8 × 3 × 2 = 48 m³, and the triangular prism volume is the area of the triangle times the length: 6 × 8 = 48 m³. Their sum is 48 + 48 = 96 m³.
A theater stage has a raised platform in the shape of a rectangular prism with dimensions 6 m × 4 m × 0.5 m. If three identical platforms are arranged in a row, what is the total volume occupied by the platforms?
36 cubic meters
30 cubic meters
42 cubic meters
24 cubic meters
First, calculate the volume of one platform: 6 × 4 × 0.5 = 12 m³. Multiplying by 3 gives 12 × 3 = 36 m³ as the total volume.
A building is composed of two sections: a rectangular block with a volume of 120 m³ and a pyramid with a base area of 30 m² and a height of 4 m. What is the combined volume of the building?
160 cubic meters
150 cubic meters
140 cubic meters
180 cubic meters
The volume of the pyramid is given by (1/3) × base area × height, which is (1/3) × 30 × 4 = 40 m³. Adding that to 120 m³ gives 120 + 40 = 160 m³.
A water fountain is designed as a composite solid consisting of a rectangular prism with dimensions 4 m × 3 m × 2 m and a semi-ellipsoid on top with semi-axes of 2 m, 1.5 m, and 1 m. Using the ellipsoid volume formula (4/3)πabc, what is the total volume of the fountain?
24 + 2π cubic meters
24 + 4π cubic meters
2π + 24 cubic meters
24π cubic meters
The rectangular prism has a volume of 4 × 3 × 2 = 24 m³. The full ellipsoid would have a volume of (4/3)π × 2 × 1.5 × 1 = 4π m³, so the semi-ellipsoid is half of that, or 2π m³. Their sum is 24 + 2π m³.
A complex container is formed by embedding a small cube with side length x inside a larger cube with side length (x + 2), leaving a hollow space between them. If the volume of the hollow space is 56 cubic units, what is the value of x?
2
3
4
1
The hollow volume is found by subtracting the volume of the inner cube from the outer cube: (x + 2)³ - x³ = 56. Expanding and simplifying yields the equation x² + 2x - 8 = 0, whose positive solution is x = 2.
A decorative fountain consists of a cylindrical basin topped with a hemispherical dome. If the cylinder's height is equal to its radius and the total volume of the structure is 150π cubic centimeters, what is the radius of the cylinder (and hemisphere)?
Cube root of 90
Cube root of 75
Cube root of 100
Cube root of 80
Let r be the radius. The cylinder's volume is πr³ (since height = r) and the hemisphere's volume is (2/3)πr³. Their sum is (5/3)πr³, which is set equal to 150π. Solving gives r³ = 90, so the radius is the cube root of 90.
An architect designs a lobby that consists of a rectangular hall with a volume of 200 m³, a cylindrical atrium with a volume of 100 m³, and a hemispherical dome with a volume of 50 m³. What is the total volume of the lobby?
350 cubic meters
300 cubic meters
400 cubic meters
250 cubic meters
By adding the volumes of all three sections - 200 m³ for the hall, 100 m³ for the atrium, and 50 m³ for the dome - the total volume is 200 + 100 + 50 = 350 cubic meters.
A sculpture is created by merging a cube and a pyramid. The cube has a side length of 3 units, and the pyramid shares the same square base (from one face of the cube) with a height of 4 units. What is the total volume of the sculpture?
39 cubic units
36 cubic units
42 cubic units
45 cubic units
The cube's volume is 3³ = 27 cubic units. The pyramid's volume is given by (1/3) × (base area) × height = (1/3) × 9 × 4 = 12 cubic units. Summing these volumes gives 27 + 12 = 39 cubic units.
0
{"name":"A small box has a volume of 24 cubic units and a larger box has a volume of 36 cubic units. What is the total volume of the two boxes?", "url":"https://www.quiz-maker.com/QPREVIEW","txt":"A small box has a volume of 24 cubic units and a larger box has a volume of 36 cubic units. What is the total volume of the two boxes?, A cube has a side length of 3 units. What is the volume of the cube?, A rectangular box has dimensions 4 units by 3 units by 2 units. What is its volume?","img":"https://www.quiz-maker.com/3012/images/ogquiz.png"}

Study Outcomes

  1. Understand the principles of adding volumes from multiple shapes.
  2. Apply volume formulas to compute the total capacity of composite objects.
  3. Analyze real-world problems involving layered or segmented objects.
  4. Calculate and verify combined volumes in multi-step geometry challenges.
  5. Evaluate problem-solving methods to ensure accuracy in volume addition tasks.

Additive Volume Worksheets Cheat Sheet

  1. Understand that volume is additive - When you combine two solid shapes, their volumes just stack together like building blocks. This means no sneaky "hidden" space - every bit counts! Embrace this idea to break complex shapes into easy chunks. Explore volume in the real world
  2. Master rectangular prism formulas - A rectangular prism's volume is simply length × width × height, so get ready to channel your inner architect. Measuring each side precisely is like gathering ingredients for the perfect cake - no guesswork! Master rectangular prism formulas
  3. Tackle composite-volume challenges - Break a funky shape into smaller prisms, calculate each piece, then add them up. It's like solving a mini-puzzle where every piece reveals part of the answer! Tackle composite-volume challenges
  4. See sandbox volume in action - Want to know how much sand you need for that beachy cube? Apply your volume skills to real-world projects and watch math come alive. It's hands-on learning at its finest! See sandbox volume in action
  5. Build with visual models - Sketch diagrams or use cubes and blocks to visualize how shapes stack and combine. These models turn abstract numbers into something you can actually see and touch! Build with visual models
  6. Check your units - Always make sure length, width, and height share the same unit - mixing inches and centimeters is a recipe for disaster. Consistent units keep your calculations smooth and error-free! Check your units
  7. Try coloring volume puzzles - Interactive coloring sheets turn practice into a game - shade regions, solve for volume, and watch vibrant patterns appear. It's a fun way to reinforce that volumes simply add up! Try coloring volume puzzles
  8. Crunch word problems - Translate everyday scenarios into volume equations to sharpen your problem-solving toolkit. Whether it's filling boxes or planning storage, these puzzles train your brain for real applications. Crunch word problems
  9. Meet volumes of various shapes - From cylinders to pyramids, get familiar with each formula so you're ready for any challenge. The more shapes you conquer, the more confident you'll feel tackling mixed-figure problems! Meet volumes of various shapes
  10. Get more practice worksheets - Consistent practice cements the concept of additive volume in your brain. Download extra worksheets and activities to level up your skills - practice makes perfect! Get more practice worksheets
Make a Quiz (FREE) Copy & Edit This Quiz Create a Quiz with AI

Mathematics Quizzes

Powered by: Quiz Maker