Learning Resources
Capacity
Interactive curriculum lessons, worked examples, and geometric problem-solving techniques designed to help Kenyan students master CBC, KPSEA, KCSE, and IGCSE mathematics.
First Principles
Objective: Master measuring and converting capacity between millilitres (\(\text{ml}\)) and litres (\(\text{L}\)).
What is Capacity? Capacity is the maximum amount of liquid a container can hold. In our daily lives—such as measuring milk from a dairy cow, pouring cooking oil, or filling a water jerrican—we measure liquid volume in metric units: litres (\(\text{L}\)) and millilitres (\(\text{ml}\)).
Interactive Jerrican & Cup Pourer
Drag the slider to pour water from the 1-Litre Jerrican into the 250 ml Cups.
Jerrican (1 L)
1000 ml
Cups Filled
0 ml
Poured: 0 L = 0 ml (0 of 4 full 250 ml cups)
Physical Intuition: The prefix milli- means one-thousandth (\(\frac{1}{1000}\)). Therefore, it takes exactly \(1000\) tiny millilitre drops or cubes to fill \(1\) standard litre container.
- Going from Litres (larger) to Millilitres (smaller): Multiply by \(1000\) (move the decimal point 3 places right).
- Going from Millilitres (smaller) to Litres (larger): Divide by \(1000\) (move the decimal point 3 places left).
Key Formulas
Fundamental Metric Identity:
\[1 \text{ L} = 1000 \text{ ml} \quad \text{and} \quad 1 \text{ ml} = \frac{1}{1000} \text{ L} = 0.001 \text{ L}\]
\[1 \text{ L} = 1000 \text{ ml} \quad \text{and} \quad 1 \text{ ml} = \frac{1}{1000} \text{ L} = 0.001 \text{ L}\]
Litres to Millilitres Conversion:
\[\text{Capacity in ml} = \text{Capacity in L} \times 1000\]
Example: \(2.45 \text{ L} \times 1000 = 2450 \text{ ml}\)
\[\text{Capacity in ml} = \text{Capacity in L} \times 1000\]
Example: \(2.45 \text{ L} \times 1000 = 2450 \text{ ml}\)
Millilitres to Litres Conversion:
\[\text{Capacity in L} = \frac{\text{Capacity in ml}}{1000}\]
Example: \(3500 \text{ ml} \div 1000 = 3.5 \text{ L}\)
\[\text{Capacity in L} = \frac{\text{Capacity in ml}}{1000}\]
Example: \(3500 \text{ ml} \div 1000 = 3.5 \text{ L}\)
Common Benchmark Equivalents:
- \(\frac{1}{4} \text{ L} = 0.25 \text{ L} = 250 \text{ ml}\) (Standard tea cup / small packet)
- \(\frac{1}{2} \text{ L} = 0.5 \text{ L} = 500 \text{ ml}\) (Standard milk packet / soda bottle)
- \(\frac{3}{4} \text{ L} = 0.75 \text{ L} = 750 \text{ ml}\) (Cooking oil bottle)
Worked Examples
Example 1 (Easy: 1-Step Conversion)
Problem: Mama Njeri bought \(3.75\) litres of fresh milk for making morning chai. How many millilitres of milk did she buy?
Problem: Mama Njeri bought \(3.75\) litres of fresh milk for making morning chai. How many millilitres of milk did she buy?
- Identify the conversion rule: Since \(1 \text{ L} = 1000 \text{ ml}\), to change from litres (larger unit) to millilitres (smaller unit), we multiply by \(1000\).
- Perform calculation: \[3.75 \times 1000 = 3750\]
Example 2 (Medium: Mixed Units & Addition)
Problem: A farmer mixes \(2.4\) litres of clean water with \(650\) millilitres of liquid foliar fertiliser in a sprayer. What is the total volume of the mixture in millilitres?
Problem: A farmer mixes \(2.4\) litres of clean water with \(650\) millilitres of liquid foliar fertiliser in a sprayer. What is the total volume of the mixture in millilitres?
- Convert all quantities to the target unit (\(\text{ml}\)): \[2.4 \text{ L} = 2.4 \times 1000 = 2400 \text{ ml}\]
- Add the amounts together: \[2400 \text{ ml} + 650 \text{ ml} = 3050 \text{ ml}\]
Example 3 (Hard: Multi-Step Division & Packaging)
Problem: A school dispensary has a \(5\)-litre container of hand sanitiser. How many \(125 \text{ ml}\) pocket bottles can be completely filled from this container?
Problem: A school dispensary has a \(5\)-litre container of hand sanitiser. How many \(125 \text{ ml}\) pocket bottles can be completely filled from this container?
- Convert container capacity into millilitres: \[5 \text{ L} = 5 \times 1000 = 5000 \text{ ml}\]
- Divide total capacity by the volume of one pocket bottle: \[\text{Number of bottles} = \frac{5000}{125}\]
- Calculate: \[5000 \div 125 = 40\]
Common Mistakes
Misconception 1 Thinking that \(1 \text{ L} = 100 \text{ ml}\) or \(10 \text{ ml}\).
Why it feels right In length, \(1 \text{ m} = 100 \text{ cm}\), and our decimal currency system uses \(100\) cents. Students often mistakenly apply the base \(100\) rule.
Correction The metric prefix milli- specifically means \(1000\). Always remember: \(1 \text{ L} = 1000 \text{ ml}\).
Misconception 2 Writing \(1 \text{ L } 50 \text{ ml}\) as \(1.5 \text{ L}\).
Why it feels right Students just write the digits after the decimal point without place value padding.
Correction Since \(50 \text{ ml} = \frac{50}{1000} \text{ L} = 0.05 \text{ L}\), \(1 \text{ L } 50 \text{ ml} = 1.05 \text{ L}\). Note that \(1.5 \text{ L} = 1500 \text{ ml}\), which is \(30\) times larger!
Misconception 3 Adding mixed units directly without converting (e.g., \(2 \text{ L} + 400 \text{ ml} = 402\)).
Why it feels right Numbers are added without aligning their measurement scales.
Correction You must always convert all quantities to the same unit before adding or subtracting: \(2 \text{ L} = 2000 \text{ ml}\), so \(2000 \text{ ml} + 400 \text{ ml} = 2400 \text{ ml}\) (or \(2.4 \text{ L}\)).
Real World
School Canteen & Juice Catering: If a caterer prepares a \(20\)-litre dispenser of passion juice for a sports day, they know it holds \(20{,}000 \text{ ml}\). Serving students in standard \(200 \text{ ml}\) cups means they can serve exactly: \[\frac{20{,}000 \text{ ml}}{200 \text{ ml}} = 100 \text{ students}\]
Agriculture & Crop Spraying: Farmers on a shamba carefully measure pesticide in millilitres (e.g., \(50 \text{ ml}\) per \(20\)-litre knapsack sprayer) to protect crops without damaging them.
Health & Medicine: Medical dosages are given in millilitres (e.g., a \(5 \text{ ml}\) spoonful of cough syrup). A \(100 \text{ ml}\) bottle contains \(20\) five-millilitre doses.
Dairy Farming: Milk sold in standard \(500 \text{ ml}\) packets means \(2\) packets make exactly \(1 \text{ litre}\).
Practice
Mama Njeri bought 3.5 litres of fresh milk from a local dairy. How many millilitres of milk did she buy?
(Type only the number, e.g., 42)
Review the concepts above.
A bottle of cough syrup at a clinic has a capacity of 750 millilitres. What is this capacity in litres?
(Type only the number, e.g., 0.5)
Review the concepts above.
Jackson is preparing juice for a school event. He mixes 1.8 litres of clean water with 650 millilitres of mango concentrate. What is the total volume of the mixture in millilitres?
(Type only the number, e.g., 42)
Review the concepts above.
The school canteen served 48 cups of fresh juice during break time. Each cup contains 250 millilitres. How many litres of juice were served in total?
(Type only the number, e.g., 15)
Review the concepts above.
A 20-litre jerrican of clean drinking water is used to fill small 400-millilitre bottles for athletes during sports day. After completely filling 35 bottles, how many litres of water remain in the jerrican?
(Type only the number, e.g., 8)
Review the concepts above.
A farmer has a 15-litre container of organic foliar spray. Each morning, she uses 750 millilitres to spray her sukuma wiki shamba. For how many full days will the container of spray last?
(Type only the number, e.g., 10)
Review the concepts above.