Volume Word Problems
Apply your volume skills to solve real-world problems about storage, shipping, construction, and more!
Why Word Problems Matter
Math in the Real World
Volume calculations are used every day by engineers, architects, shipping companies, aquarium keepers, and many more professionals. Learning to solve word problems prepares you to apply math to real situations!
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Shipping & Storage
How much can fit in a box or container?
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Pools & Tanks
How much water is needed?
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Construction
How much concrete or material?
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Gardening
How much soil for a planter?
Problem-Solving Strategy
CUBES Method for Word Problems
C
Circle the numbers
U
Underline the question
B
Box key words
E
Evaluate & draw
S
Solve & check
Key Words to Look For:
- Volume, capacity, holds, fills, contains - Find volume (multiply l x w x h)
- How much space, cubic - Volume calculation
- Total, combined, altogether - May need to add volumes
- Remaining, left over, difference - May need to subtract
Worked Examples
Example 1: Shipping Box
Maria is shipping books in a cardboard box. The box is 18 inches long, 12 inches wide, and 10 inches tall. She wants to know how much packing material she can add around the books if the books take up 1,500 cubic inches of space.
Solution
1 Identify what we need to find
We need to find: Space remaining for packing material = Total box volume - Book volume
2 Find the box volume
V = l x w x h
V = 18 x 12 x 10 = 2,160 in³
3 Subtract the book volume
Space for packing = Box volume - Book volume
Space = 2,160 - 1,500 = 660 in³
Maria can add up to 660 cubic inches of packing material.
Example 2: Swimming Pool
A rectangular swimming pool is 25 meters long, 10 meters wide, and 2 meters deep. If water costs $0.50 per cubic meter, how much will it cost to fill the pool?
Solution
1 Find the pool volume
V = l x w x h
V = 25 x 10 x 2 = 500 m³
2 Calculate the cost
Cost = Volume x Price per cubic meter
Cost = 500 x $0.50 = $250.00
It will cost $250 to fill the pool.
Example 3: L-Shaped Room
An L-shaped living room needs to be air-conditioned. The main section is 20 feet long, 15 feet wide, and 9 feet tall. The smaller section is 10 feet long, 8 feet wide, and 9 feet tall. An air conditioner can cool 500 cubic feet per minute. How long will it take to fully cool the room?
Solution
1 Find volume of main section
V1 = 20 x 15 x 9 = 2,700 ft³
2 Find volume of smaller section
V2 = 10 x 8 x 9 = 720 ft³
3 Find total volume
Total = 2,700 + 720 = 3,420 ft³
4 Calculate cooling time
Time = Total volume / Cooling rate
Time = 3,420 / 500 = 6.84 minutes
It will take about 7 minutes to cool the room.
Practice Problems
Solve these word problems. Choose the correct answer!
Problem 1 Easy
A fish tank is 30 inches long, 12 inches wide, and 18 inches tall. What is the volume of the tank?
Problem 2 Easy
A gift box is a cube with sides of 8 inches. What is its volume?
Problem 3 Medium
A storage container holds 1,200 cubic feet. It is 15 feet long and 8 feet wide. How tall is it?
Problem 4 Medium
A concrete slab is 20 feet long, 12 feet wide, and 6 inches (0.5 feet) thick. If concrete costs $100 per cubic foot, what is the total cost?
Problem 5 Medium
A raised garden bed is 6 feet long, 4 feet wide, and 1.5 feet deep. How many cubic feet of soil are needed to fill it?
Problem 6 Hard
A moving truck is 16 feet long, 8 feet wide, and 7 feet tall. A family has boxes that total 750 cubic feet. How much space is left in the truck?
Problem 7 Hard
A T-shaped building has a top section (30 m x 8 m x 10 m) and a stem section (10 m x 15 m x 10 m). What is the total volume of the building?
Problem 8 Hard
A wading pool is 12 ft x 8 ft x 3 ft deep. Water is being pumped in at 6 cubic feet per minute. How many minutes will it take to fill the pool?
Problem 9 Hard
A rectangular room is 14 ft x 12 ft x 8 ft. An air purifier cleans 80 cubic feet of air per hour. How many hours to clean all the air in the room?
Problem 10 Hard
A storage unit is 10 ft x 10 ft x 8 ft. Small boxes (2 ft x 2 ft x 2 ft) are stacked inside. What is the maximum number of small boxes that can fit?
What We Learned
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Read Carefully
Identify numbers and what the question asks
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Key Words
Look for volume, capacity, holds, fills
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Apply Formula
V = l x w x h for rectangular prisms
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Check Units
Make sure your answer makes sense!
Pro Tip: Real-world problems often require multiple steps. After finding the volume, you might need to multiply (for cost) or divide (for time or quantity). Always re-read the question to make sure you answered what was asked!
Next Steps
- Move on to Common Mistakes to learn what to avoid
- Look for volume problems in everyday life
- Try creating your own word problems
- Practice multi-step problems for test preparation