094r. Capacity and Volume Conversions

Learning Intentions

• To understand that capacity is the volume of fluid or gas that an object can hold
• To know that common metric units include millilitres, litres, kilolitres and megalitres
• convert between common units for capacity
• convert between the volume and capacity of a container

Pre-requisite Summary

• Know that volume measures the amount of space inside a three-dimensional object
• Know that capacity measures how much fluid or gas a container can hold
• Know that capacity is commonly measured in $\text{mL},\text{L},\text{kL}$ and $\text{ML}$
• Know that $1000\text{ mL}=1\text{ L}$
• Know that $1000\text{ L}=1\text{ kL}$
• Know that $1000\text{ kL}=1\text{ ML}$
• Know that $1{\text{ cm}}^3=1\text{ mL}$
• Know that $1000{\text{ cm}}^3=1\text{ L}$
• Know that $1{\text{ m}}^3=1000\text{ L}=1\text{ kL}$
• Know that converting to a smaller unit makes the number larger, and converting to a larger unit makes the number smaller

Worked Examples

Worked Example 1

State whether each measurement would usually describe volume or capacity.
a) The amount of water a bottle can hold
b) The space inside a solid block
c) The amount of juice in a carton

Worked Example 2

Convert the following capacities.
a) $3\text{ L}$ to $\text{mL}$
b) $4500\text{ mL}$ to $\text{L}$
c) $2.5\text{ kL}$ to $\text{L}$

Worked Example 3

Convert the following capacities.
a) $0.8\text{ L}$ to $\text{mL}$
b) $7200\text{ L}$ to $\text{kL}$
c) $1.6\text{ ML}$ to $\text{kL}$

Worked Example 4

A fish tank has volume $24000{\text{ cm}}^3$. Find its capacity in millilitres and litres.

Worked Example 5

A water tank has volume $3.2{\text{ m}}^3$. Find its capacity in litres and kilolitres.

Worked Example 6

A container has capacity $1.5\text{ L}$. Express this as a volume in ${\text{cm}}^3$.

Problems

Problem 1

State whether each measurement would usually describe volume or capacity.
a) The amount of petrol a car tank can hold
b) The space inside a brick
c) The amount of milk in a jug

Problem 2

Convert the following capacities.
a) $5\text{ L}$ to $\text{mL}$
b) $6800\text{ mL}$ to $\text{L}$
c) $4.2\text{ kL}$ to $\text{L}$

Problem 3

Convert the following capacities.
a) $1.4\text{ L}$ to $\text{mL}$
b) $9500\text{ L}$ to $\text{kL}$
c) $2.3\text{ ML}$ to $\text{kL}$

Problem 4

A container has volume $18000{\text{ cm}}^3$. Find its capacity in millilitres and litres.

Problem 5

A tank has volume $4.5{\text{ m}}^3$. Find its capacity in litres and kilolitres.

Problem 6

A container has capacity $2.8\text{ L}$. Express this as a volume in ${\text{cm}}^3$.

Exercises

Understanding and Fluency

1. Decide whether each statement is about volume or capacity.
   a) The amount of liquid a bottle can hold
   b) The amount of space inside a cube
   c) The amount of water in a bucket

2. Choose the most suitable unit for each capacity.
   a) A medicine spoon
   b) A drink bottle
   c) A backyard swimming pool

3. Complete the conversions.
   a) $1\text{ L}=\mathrm{\_}\mathrm{\_}\mathrm{\_}\text{ mL}$
   b) $1\text{ kL}=\mathrm{\_}\mathrm{\_}\mathrm{\_}\text{ L}$
   c) $1\text{ ML}=\mathrm{\_}\mathrm{\_}\mathrm{\_}\text{ kL}$

4. Convert the following.
   a) $2\text{ L}$ to $\text{mL}$
   b) $7\text{ L}$ to $\text{mL}$
   c) $0.5\text{ L}$ to $\text{mL}$

5. Convert the following.
   a) $3500\text{ mL}$ to $\text{L}$
   b) $1250\text{ mL}$ to $\text{L}$
   c) $900\text{ mL}$ to $\text{L}$

6. Convert the following.
   a) $6\text{ kL}$ to $\text{L}$
   b) $8400\text{ L}$ to $\text{kL}$
   c) $2.7\text{ ML}$ to $\text{kL}$

7. Convert between volume and capacity.
   a) $500{\text{ cm}}^3$ to $\text{mL}$
   b) $2500{\text{ cm}}^3$ to $\text{L}$
   c) $1.2{\text{ m}}^3$ to $\text{kL}$

8. Convert between volume and capacity.
   a) $3\text{ L}$ to ${\text{cm}}^3$
   b) $750\text{ mL}$ to ${\text{cm}}^3$
   c) $2\text{ kL}$ to ${\text{m}}^3$

Reasoning

9. Explain why capacity is often used for containers, while volume is often used for solids.

10. A student says $1{\text{ cm}}^3=1\text{ L}$. Explain why this is incorrect.

11. Explain why $1{\text{ m}}^3=1\text{ kL}$.

12. A student converts $4.5\text{ L}$ to millilitres and gets $0.0045\text{ mL}$. Describe the mistake.

Problem-solving

13. A juice carton holds $2\text{ L}$. How many millilitres is this?

14. A rainwater tank has capacity $5\text{ kL}$. How many litres can it hold?

15. A reservoir holds $3.4\text{ ML}$ of water. Express this in kilolitres.

16. A rectangular fish tank has volume $36000{\text{ cm}}^3$. What is its capacity in litres?

17. A water trough has volume $1.8{\text{ m}}^3$. What is its capacity in litres?

18. A bottle has capacity $600\text{ mL}$. Express this as a volume in ${\text{cm}}^3$.

Potential Misunderstandings

• A student may confuse capacity with volume and think they always refer to exactly the same idea
• A student may not recognise that capacity usually refers to how much fluid or gas a container can hold
• A student may think converting between capacity units uses addition or subtraction instead of multiplication or division by powers of $10$
• A student may reverse the direction of conversion when moving between larger and smaller units
• A student may think $1{\text{ cm}}^3=1\text{ L}$ instead of $1{\text{ cm}}^3=1\text{ mL}$
• A student may not know that $1000{\text{ cm}}^3=1\text{ L}$
• A student may confuse $1{\text{ m}}^3=1000\text{ L}$ with $1{\text{ m}}^3=1\text{ L}$
• A student may omit units or use volume units when capacity units are expected, and vice versa