DoAssignment study guide
E2.1 · Relate volume in cubic centimetres to capacity in millilitres
Learn to relate volume in cubic centimetres to capacity in millilitres through clear examples and targeted practice.
Ontario Grade 7 Mathematics
Spatial Sense
Connecting the space inside a container to the liquid it can hold
Imagine a small cube that is 1 centimetre long, 1 centimetre wide, and 1 centimetre high. Its volume is 1 cubic centimetre. That same amount of space is equal to a capacity of 1 millilitre. This link lets us describe the inside space of a container in two related ways: as cubic centimetres or as millilitres.
What you will learn
- Explain what volume and capacity mean in a container example.
- Relate one cubic centimetre to one millilitre.
- Use the relationship to describe and compare volume and capacity.
Start with space and liquid
Volume tells how much space a solid object or container takes up. For a container, we can focus on the space inside it. Capacity tells how much the container can hold.
A cubic centimetre is a unit of volume. It is the space inside a cube with each edge 1 centimetre long. The short form is cm³. A millilitre is a unit used to describe the capacity of a container. Its short form is mL.
Picture filling a container with tiny cubes, each measuring 1 cm on every edge. One such cube takes up 1 cm³ of space. The amount of liquid that fills that same space is 1 mL. So the units match one for one.
- Volume describes space.
- Capacity describes how much a container can hold.
- One cubic centimetre is equal to one millilitre.
Use the one-to-one relationship
Because each cubic centimetre matches one millilitre, the number stays the same when you change from cm³ to mL. For example, 8 cm³ of space corresponds to 8 mL of capacity.
The same relationship works in reverse. A capacity of 12 mL corresponds to 12 cm³ of volume. The unit changes, but the amount represented does not.
A container’s stated capacity describes how much it can hold when full. If it is only partly filled, the amount of liquid in it can be less than its capacity. The one-to-one relationship still applies to the space occupied by the liquid.
- To relate cm³ and mL, keep the numerical value and change the unit.
- Check whether the question asks for volume or capacity so you choose the correct unit.
Read a labelled model
A small rectangular container can be pictured as a stack of unit cubes. A unit cube is a cube measuring 1 cm along each edge. If the container’s inside space holds 24 such cubes, that space is 24 cm³. The matching capacity is 24 mL.
The model shows why the numerical values match: each unit cube represents 1 cm³, and each one corresponds to 1 mL. You do not need to count physical cubes when a volume or capacity is already given.
- Each unit cube represents 1 cm³.
- The same amount of space corresponds to 1 mL of capacity.
Practise choosing the unit
First decide what the question describes. If it asks for the space inside a container in cubic centimetres, use cm³. If it asks how much liquid the container can hold in millilitres, use mL.
Then use the one-to-one relationship. Keep the number unchanged and write the requested unit. For instance, a space of 35 cm³ matches 35 mL of capacity.
Before finishing, check that the unit answers the question. A correct number with the wrong unit does not fully answer it.
- Identify whether the question asks for volume or capacity.
- Keep the numerical value the same when relating cm³ and mL.
- Write the unit that matches the question.
Matching volume and capacity
| Volume | Matching capacity |
|---|---|
| 1 cm³ | 1 mL |
| 8 cm³ | 8 mL |
| 24 cm³ | 24 mL |
Worked example
Volume to capacity
A small container has an inside volume of 18 cm³. What is its matching capacity in millilitres?
A container with an inside volume of 18 cm³ has a matching capacity of 18 mL. The solid is schematic, not a measured drawing.
- Name the relationshipEach cubic centimetre corresponds to one millilitre, so the number stays the same.
- Change to the requested unitThe question asks for capacity, so express the matching amount in millilitres.
Answer: The matching capacity is 18 mL.
Check: The number is unchanged, and mL is the requested capacity unit.
Worked example
Capacity to volume
A cup can hold 27 mL when full. What volume in cubic centimetres matches that capacity?
A full cup with capacity 27 mL matches an inside volume of 27 cm³. The solid is schematic, not a measured drawing.
- Identify the requested quantityThe question asks for volume, so the answer needs the unit cm³.
- Use the matching amountMillilitres and cubic centimetres match one for one. Keep 27 and change the unit to cubic centimetres.
Answer: The matching volume is 27 cm³.
Check: The answer uses cm³ for volume and keeps the same numerical value.
Worked example
Compare two amounts
Container A has an inside volume of 16 cm³. Container B has a capacity of 19 mL. Which amount is greater, and by how much in matching units?
- Use the same unitCompare the amounts only after they are written in matching units. The capacity of B is already in millilitres, and A’s volume matches the same number of millilitres.
- Compare the numbersNow compare 16 mL and 19 mL. The amount for B is greater. The difference is 3 mL.
Answer: Container B’s amount is greater by 3 mL.
Check: In matching units, 19 mL is greater than 16 mL.
Common mistakes and how to avoid them
Changing the number when changing from cm³ to mL.
Correction: The relationship is one for one. Keep the number and change only the unit.
Using cm³ when a question asks for capacity in mL.
Correction: Check the question’s wording, then write the unit it requests.
Thinking a partly filled container has its full capacity of liquid inside it.
Correction: Capacity tells how much the container can hold when full. A partly filled container holds less than its full capacity.
Lesson summary
- Volume describes space; capacity describes how much a container can hold.
- One cubic centimetre corresponds to one millilitre.
- When relating cm³ and mL, the number stays the same.
- Use the unit that matches what the question asks.
Check your understanding
Question 1
A container has an inside volume of 31 cm³. What is its matching capacity?
- 31 mL
- 13 mL
- 310 mL
- 31 cm³
Show answer and explanation
31 mL
Each cubic centimetre matches one millilitre, so 31 cm³ matches 31 mL.
Question 2
A small bottle has a capacity of 6 mL. What volume matches it?
- 60 cm³
- 6 cm³
- 3 cm³
- 6 mL
Show answer and explanation
6 cm³
The numerical value stays 6, and the requested volume unit is cm³.
Key terms
- Volume
- The amount of space an object or container takes up.
- Capacity
- The amount a container can hold when full.
- Cubic centimetre
- A unit of volume equal to the space inside a cube with edges 1 centimetre long; written cm³.
- Millilitre
- A unit used to describe capacity; written mL.
- Unit cube
- A cube that measures 1 centimetre along each edge when used to model 1 cm³.
Continue through Grade 7 Math
View the complete Grade 7 Math Ontario Grade 7 Mathematics curriculum and lessons
- E1.4 · Translate, reflect, and rotate shapes on a Cartesian plane
- E2.2 · Convert metric units in perimeter, area, and volume problems
- E1.1 · Classify cylinders, pyramids, and prisms by properties and symmetry
- E1.2 · Draw scaled top, front, side, and perspective views
- E1.3 · Perform dilations and describe similar shapes
- E2.3 · Connect radius, diameter, and circumference
About this lesson and its review
Published by DoAssignment. This reviewed lesson follows Ontario Grade 7 Mathematics, expectation E2.1. It is a study resource, not an official curriculum publication.
Before publication, content is checked for structure, mathematical or chemical notation, calculations, course boundaries, and readability. Errors can still occur, so corrections are welcomed.