6th grade · Math · Unit 8 of 21
Volume & Capacity
Cubes, liters and milliliters
What your child practices
Finding the volume of rectangular prisms, converting between liters and milliliters, and connecting volume to capacity (1 cm³ holds 1 mL).
New York State Learning Standards learning standard: NY-6.G.2 · volume of right rectangular prisms
How we explain it
Children can open this short lesson before they practice.
- Volume is the space inside a solid, in cubic units like cm³.
- Volume of a rectangular prism = length × width × height.
- 1 cm³ holds 1 mL. 1000 mL is 1 L.
Example: A box is 5 cm long, 4 cm wide and 3 cm high. What is its volume? 5 × 4 = 20. 20 × 3 = 60. Answer: 60 cm³
Volume & Capacity in New York
In the New York State Learning Standards, this is unit 8 of 21 in 6th grade Math, after Perimeter & Area and before Probability.
Gradelings describes a child's practice on this unit as Beginning, Approaching, Meeting or Exceeding (Four practice steps). That reflects practice, not a report-card mark: the teacher decides the mark.
Sample questions
A taste of this unit. In the app, questions change every time and get easier or harder to match your child.
Question 1
This is the bottom layer of a box packed with 1 cm cubes. The box is 6 layers high. What is the volume of the box?
🧊🧊🧊🧊🧊🧊🧊🧊🧊🧊🧊🧊answer boxcm³
72 cm³
Hint: Find the number of cubes in one layer (rows × columns), then multiply by the number of layers.
Question 2
Which box has the greatest volume?
- 7 cm × 9 cm × 7 cm
- 6 cm × 6 cm × 4 cm
- 9 cm × 9 cm × 6 cm
- 5 cm × 2 cm × 2 cm
9 cm × 9 cm × 6 cm
Hint: Work out each volume (length × width × height), then compare. A box can be longer but still hold less.
Question 3
A jug holds 5.5 L of lemonade. How many 500 mL glasses can it fill?
🍋5.5 Lanswer box
11
Hint: Change liters to milliliters (× 1000), then divide by 500.
Question 4
A box has a volume of 100 cm³. It is 10 cm long and 5 cm wide. How high is it?
answer boxcm
2 cm
Hint: Volume = length × width × height. The base is 10 × 5 = 50 cm², so divide the volume by 50.
Question 5
Which unit is best for measuring the volume of a shipping container?
- square meters (m²)
- milliliters (mL)
- cubic centimeters (cm³)
- cubic meters (m³)
cubic meters (m³)
Hint: Volume is measured in cubic units. A shipping container is huge, so use meter cubes.
Question 6
A rectangular prism is 8 cm long, 8 cm wide and 12 cm high. What is its volume?
answer boxcm³
768 cm³
Hint: Volume = length × width × height. Multiply two of the numbers first, then multiply by the third.