Measuring Volume and Capacity (Grade 12 NSC Matric Mathematical Literacy): Revision Notes
Measuring Volume and Capacity
Understanding volume and capacity
Volume is a measurement that tells us how much space an object takes up. Capacity is a measurement that tells us how much liquid a container can hold when it is completely full.
These two concepts are closely related but have an important difference. Think of a 500 ml bottle of cola with 200 ml of cola left inside it. The capacity of the bottle is 500 ml (the maximum it can hold), while the volume of cola currently inside is 200 ml.
Understanding this distinction is essential for solving real-world problems. Volume tells us what's actually there, while capacity tells us the maximum potential. This difference becomes crucial when calculating how many containers you need or how much liquid remains.
Key units and conversions
The most common units for measuring volume and capacity are:
- Millilitres (ml) - for smaller quantities
- Litres (ℓ) - for larger quantities
Essential conversion to memorise:
When working with volume problems, always convert to the same units before calculating. This prevents calculation errors and ensures accurate results.
Worked example 1: Water urn calculations
Worked Example: Office Water Urn Problems
An office water urn has a capacity of 20 litres. Let's solve several related problems:
Problem 1: If the urn is filled to maximum capacity, how many 250 ml cups can be poured from it?
Solution:
- Convert capacity to ml:
- Divide by cup size:
- Answer: 80 cups can be poured from the urn
Problem 2: After morning tea, only 6 litres of water remain. How many 250 ml cups are left?
Solution:
- Convert remaining water to ml:
- Divide by cup size:
- Answer: 24 cups of water remain
Problem 3: What percentage of the urn's capacity is the remaining 6 litres?
Solution:
- Calculate percentage:
- Answer: The urn is 30% full
Worked example 2: Soil transportation
Worked Example: Moving Soil with Buckets
Jabu needs to move 300 litres of soil using a 10-litre bucket. How many trips will this take?
Solution:
- Divide total volume by bucket capacity:
- Answer: Jabu needs to make 30 trips
Alternative scenario: If Jabu only fills the bucket with 7 litres each trip, how many trips are needed?
Solution:
- Divide total by actual amount per trip:
- Since partial trips aren't possible, round up to 43 trips
- Answer: 43 trips needed (the last trip won't have a full 7 litres)
Notice how we must round up when dealing with real-world constraints. You can't make 0.8 of a trip, so we need a complete additional trip even if it's not completely full.
Worked example 3: Cost calculations with paraffin
Worked Example: Paraffin Cost Calculations
Paraffin costs R7.80 per litre at a service station.
Problem 1: How much will 5 litres of paraffin cost?
Solution:
- Use the formula: Number of litres × Cost per litre
- Answer: R39
Problem 2: How many litres can you buy for R20?
Solution:
- Use the formula: Amount of money ÷ Cost per litre
- Rounded to two decimal places: 2.56 litres
Problem 3: If you have a 500 ml paraffin lamp and buy 3 litres, how many times can you refill it?
Solution:
- Convert 3 litres to ml:
- Divide by lamp capacity:
- Answer: You can refill the lamp 6 times
Worked example 4: Petrol cost calculations
Worked Example: Petrol Purchase Calculations
Petrol costs R10.72 per litre.
Problem 1: How much does it cost to fill a 50-litre tank?
Solution:
- Number of litres × Cost per litre
- Answer: R536
Problem 2: How many litres can you buy with R200?
Solution:
- Amount of money ÷ Cost per litre
- Rounded to two decimal places: 18.66 litres
Cost and volume calculations from activities
Here are solutions to typical volume and cost problems you might encounter. These demonstrate how to apply the concepts in practical situations:
| Problem | Solution | Points |
|---|---|---|
| Converting 1⅓ cups of milk to ml (1 cup = 250 ml) | 333 ml of milk | 1 |
| Amount of milk needed for 30 cupcakes if recipe for 20 needs 500 ml | 0.5 ℓ (or 750 ml total) | 2 |
| Cost of milk for 30 cupcakes at R8.50 per litre | R8.50 (only need half bottle) | 1 |
| Business Problem | Solution | Points |
|---|---|---|
| Cups of lemonade from 5 litres (250 ml cups) | 20 cups | 1 |
| Revenue from selling 20 cups at R5 each | R100 | 1 |
| Break-even point if costs are R120 | Need to sell 24 cups | 1 |
These table problems show how volume and capacity calculations connect to real-world scenarios like cooking and small business operations. Notice how we sometimes need to buy more than we actually use (like buying a full litre when we only need 500 ml).
Exam tips and common traps
Common mistakes to avoid:
- Forgetting to convert units before calculating
- Not rounding appropriately for real-world contexts
- Confusing volume with capacity in word problems
- Using the wrong formula for cost calculations
Always remember: You can't have 0.8 of a trip or buy 0.3 of a container in real life!
Essential formulas for cost calculations:
- Total cost = Number of litres × Cost per litre
- Quantity you can buy = Available money ÷ Cost per litre
- Number of portions = Total volume ÷ Size of each portion
Key Points to Remember:
- Volume measures space taken up; capacity measures maximum liquid a container can hold when full
- Always convert to the same units before calculating:
- For cost problems: multiply to find total cost, divide to find how much you can buy
- Round answers sensibly - you can't have partial trips or partial containers in real life
- Double-check your conversions between ml and litres to avoid calculation errors