HSPT: Volume: from cubic centimeters to liters
Learn to find the volume of a box-shaped container and convert it from cubic centimeters to liters.
How do you find how many liters a box-shaped container holds?
Short answer
Multiply length × width × height to get cubic centimeters. Then divide by 1,000, since 1 liter = 1,000 cm³.
Know first: Multiplying whole numbers, Dividing by 1,000
Step 1 of 5
Find the volume, then convert to liters
The volume of a box-shaped container is length × width × height. If the measurements are in centimeters, the volume is in cubic centimeters, written cm³.
To change cubic centimeters to liters, use 1 liter = 1,000 cm³. Since a liter is the bigger unit, the number of liters is smaller: divide by 1,000.
| Cubic centimeters | Divide by 1,000 | Liters |
|---|---|---|
| 1,000 cm³ | 1,000 ÷ 1,000 | 1 L |
| 500 cm³ | 500 ÷ 1,000 | 0.5 L |
| 2,500 cm³ | 2,500 ÷ 1,000 | 2.5 L |
| 250 cm³ | 250 ÷ 1,000 | 0.25 L |
Dividing by 1,000 moves the decimal point three places left.
Step 2 of 5
Multiply three dimensions, divide by 1,000
Worked example: A storage bin
A box-shaped bin measures 40 cm by 25 cm by 16 cm inside. Using 1 liter = 1,000 cm³, how many liters does it hold?
- A16
- B160
- C1.6
- D0.081
- 1
Volume
40 × 25 × 16. Start with 40 × 25 = 1,000, then 1,000 × 16 = 16,000 cm³.
- 2
Convert
16,000 ÷ 1,000 = 16 liters.
- 3
Sense check
A bin about the size of a small suitcase holding 16 liters is reasonable.
- 4
See why the other choices are there
160 divides by 100 instead of 1,000. 1.6 divides by 10,000. 0.081 adds the three measurements, 81, then divides by 1,000.
Answer
16 liters
Find the wrong step
A student finds the capacity of a 12 cm by 5 cm by 9 cm box in liters.
- 1
Multiplies: 12 × 5 × 9 = 540 cm³.
- 2
Multiplies by 1,000 to change to liters: 540,000 liters.
What went wrong
A liter is much bigger than a cubic centimeter, so the number of liters must be smaller. Divide by 1,000.
- 3
Answers 540,000 liters.
The fix
540 ÷ 1,000 = 0.54 liters.
Step 3 of 5
Volume first, then the conversion
Check yourself · Question 1
A tank measures 60 cm by 40 cm by 25 cm inside. Using 1 liter = 1,000 cm³, what is its capacity in liters?
Answer: B
Volume: 60 × 40 × 25. Since 40 × 25 = 1,000, the volume is 60 × 1,000 = 60,000 cm³. Divide by 1,000: 60 liters.
Trap answer: 600
Dividing by the wrong power of ten
- Why it looks right
- Dropping two zeros is quick, and 600 looks like a reasonable size for a tank.
- Why it's wrong
- 1 liter is 1,000 cm³, so the decimal point moves three places, not two.
- The right answer
- 60 liters
Check yourself · Question 2
A fish tank is 40 cm long and 25 cm wide, and 50 cm tall. It is filled with water to a depth of 35 cm. Using 1 liter = 1,000 cm³, how many liters of water are in it?
Answer: C
Use the water's depth as the height: 40 × 25 × 35 = 1,000 × 35 = 35,000 cm³. Divide by 1,000: 35 liters.
Common mistake
"Liters are the answer unit, so I multiply by 1,000."
- Why it's tempting
- Converting often feels like it should make the number bigger.
- Do this instead
- Ask which unit is bigger. A liter holds 1,000 cm³, so a volume in liters is the smaller number: divide.
Step 4 of 5
What to remember
Remember
- Volume of a box is length × width × height, in cm³ when the sides are in cm.
- Divide cubic centimeters by 1,000 to get liters.
- If a container is only partly full, use the depth of the contents as the height.
Step 5 of 5
Practice on a real question
Use what you just learned on this question, then check the explanation.
In your own words
What was the volume in cubic centimeters in the practice question, and which choice comes from forgetting to divide by 1,000?