Solved Exercises on Liquid Volume and Mass in Grade 3

Master the relationship between liquid volume and mass: understanding measurements, conversions, and real-world applications through these 5 detailed exercises.

Solution: Exercises 1 to 3
1 Basic Liquid Volume Measurement
Exercise 1
A jug contains 2.5 L of water. If 750 mL of water is poured out, how much water remains in the jug?
Definition:

Liquid Volume: The amount of space a liquid takes up, measured in liters (L) or milliliters (mL).

Volume Subtraction: Finding the remaining volume by subtracting the poured amount from the initial volume.

Liquid Volume Method:
  1. Convert all volumes to the same unit
  2. Subtract the poured volume from the initial volume
  3. Express the result in the desired unit
Step 1: Convert all volumes to the same unit

Initial water: 2.5 L = 2.5 × 1,000 = 2,500 mL
Poured water: 750 mL

Step 2: Subtract the poured volume from initial volume

Remaining water = 2,500 mL - 750 mL = 1,750 mL

Step 3: Convert back to liters if needed

1,750 mL = 1,750 ÷ 1,000 = 1.75 L

Remaining water: 1,750 mL (or 1.75 L)
Final answer:

There are 1,750 mL (or 1.75 L) of water remaining in the jug.

Applied rules:

• Unit Conversion: 1 L = 1,000 mL

• Volume Subtraction: Remaining = Initial - Removed

• Conservation: Total volume decreases when liquid is removed

2 Liquid Mass Calculation
Exercise 2
If 1 liter of water has a mass of 1 kg, what is the mass of 3.5 L of water?
Definition:

Mass: The amount of matter in an object, measured in grams (g) or kilograms (kg).

Water Density: 1 L of water has a mass of 1 kg (1,000 g).

Step 1: Understand the relationship between volume and mass

1 L of water = 1 kg of mass

Step 2: Calculate the mass for the given volume

3.5 L of water = 3.5 × 1 kg = 3.5 kg

Step 3: Convert to grams if needed

3.5 kg = 3.5 × 1,000 = 3,500 g

Mass of water: 3.5 kg (or 3,500 g)
Final answer:

The mass of 3.5 L of water is 3.5 kg (or 3,500 g).

Applied rules:

• Water Density: 1 L = 1 kg

• Proportional Relationship: Volume and mass are directly proportional for water

• Unit Conversion: 1 kg = 1,000 g

3 Volume-Mass Relationship
Exercise 3
A container holds 2 L of juice. If the juice has the same density as water, what is the mass of the juice in grams?
Definition:

Density: The relationship between volume and mass. For water-like substances, 1 L ≈ 1 kg.

Volume-Mass Conversion: Using the density relationship to convert between volume and mass.

Step 1: Identify the volume of liquid

Volume of juice = 2 L

Step 2: Apply the density relationship

Since juice has the same density as water:
1 L of juice = 1 kg of mass
2 L of juice = 2 kg of mass

Step 3: Convert to grams

2 kg = 2 × 1,000 = 2,000 g

Mass of juice: 2,000 g
Final answer:

The mass of 2 L of juice is 2,000 grams.

Applied rules:

• Density Assumption: Equal density means equal volume-mass ratio

• Direct Proportion: Volume and mass increase proportionally

• Unit Conversion: 1 kg = 1,000 g

Liquid Volume and Mass Rules and Methods
1 L = 1 kg (for water)
Volume-Mass Relationship
Volume Conversion
1 L = 1,000 mL
Convert between units
Mass Conversion
1 kg = 1,000 g
Convert between units
Water Density
1 L = 1 kg
Volume-mass relationship
Key Definitions:

Liquid Volume (L/mL): The space occupied by a liquid, measured in liters or milliliters.

Mass (g/kg): The amount of matter in an object, measured in grams or kilograms.

Density: The relationship between volume and mass of a substance.

Water Relationship: 1 L of water = 1 kg of mass
Unit Conversion: Always convert to same units before calculations
Proportional Reasoning: Volume and mass are directly proportional for water
Tip 1: Remember: 1 L = 1,000 mL and 1 kg = 1,000 g
Tip 2: For water-like liquids: Volume in L = Mass in kg
Tip 3: Always check units before performing calculations
Solution: Exercises 4 to 5
4 Mixed Units Problem
Exercise 4
A recipe calls for 750 mL of milk and 250 mL of cream. If both liquids have the same density as water, what is the total mass of the liquids in grams?
Definition:

Mixed Unit Problems: Calculations involving different units that need to be converted before processing.

Step 1: Add the volumes together

Milk: 750 mL
Cream: 250 mL
Total volume: 750 + 250 = 1,000 mL

Step 2: Convert volume to liters

1,000 mL = 1,000 ÷ 1,000 = 1 L

Step 3: Calculate mass using density relationship

Since density is same as water:
1 L = 1 kg of mass

Step 4: Convert mass to grams

1 kg = 1 × 1,000 = 1,000 g

Total mass: 1,000 g
Final answer:

The total mass of the liquids is 1,000 grams.

Applied rules:

• Volume Addition: Sum all volumes before mass calculation

• Density Application: Use volume-mass relationship

• Unit Conversion: Convert to final required unit

5 Real-World Application
Exercise 5
A large water tank contains 15 L of water. If a family drinks 3.5 L of water in one day, what is the mass of the remaining water in kilograms?
Definition:

Real-World Applications: Using mathematical concepts to solve practical problems involving volume and mass.

Step 1: Calculate the remaining volume

Initial water: 15 L
Water consumed: 3.5 L
Remaining water: 15 - 3.5 = 11.5 L

Step 2: Apply the volume-mass relationship

Since water density is 1 L = 1 kg:
11.5 L = 11.5 kg

Step 3: Verify the calculation

Initial mass: 15 L = 15 kg
Consumed mass: 3.5 L = 3.5 kg
Remaining mass: 15 - 3.5 = 11.5 kg ✓

Remaining mass: 11.5 kg
Final answer:

The mass of the remaining water is 11.5 kilograms.

Applied rules:

• Volume Subtraction: Remaining = Initial - Consumed

• Mass Conservation: Mass decreases proportionally with volume

• Verification: Check calculations for accuracy

Key Concepts: Liquid Volume and Mass, Definitions, Methods, and Formulas
1 L = 1 kg (for water)
Volume-Mass Relationship
Key definitions:

Liquid Volume: The amount of space a liquid occupies, measured in liters (L) or milliliters (mL).

Mass: The amount of matter in an object, measured in grams (g) or kilograms (kg).

Density: The relationship between volume and mass of a substance.

Complete methodology:
  1. Identify units: Determine the units of volume and mass in the problem
  2. Convert if necessary: Change all measurements to the same unit
  3. Apply relationships: Use volume-mass relationships (e.g., 1 L = 1 kg for water)
  4. Perform calculation: Add, subtract, or multiply as required
  5. Express answer: State the result in the required unit
Tip 1: Remember: 1 L = 1,000 mL and 1 kg = 1,000 g
Tip 2: For water-like liquids: Volume in L = Mass in kg
Tip 3: Always convert to same units before calculations
Tip 4: Check your work by verifying calculations

Common errors: Forgetting to convert units, confusing volume with mass, misapplying density relationships.
Practice activities: Measure liquids with graduated cylinders, weigh water samples, solve real-world problems.
Formulas to know by heart:

• Unit Conversions: 1 L = 1,000 mL; 1 kg = 1,000 g

• Water Density: 1 L of water = 1 kg of mass

• Volume Operations: Add/subtract volumes in same units

• Mass Operations: Mass changes proportionally with volume

Exercise with Visualization: Water Consumption
Exercise 6: Daily Water Tracking
A student tracks their daily water consumption:
Morning: 250 mL
Lunch: 500 mL
Afternoon: 350 mL
Evening: 400 mL
What is the total volume in liters and the total mass in grams?

Analysis: Add all volumes and convert to find mass.

  • Morning: 250 mL
  • Lunch: 500 mL
  • Afternoon: 350 mL
  • Evening: 400 mL
  • Total: 250 + 500 + 350 + 400 = 1,500 mL = 1.5 L
  • Mass: 1.5 L = 1.5 kg = 1,500 g

Questions & Answers

Question: My 3rd grade students often confuse liquid volume with mass. How can I help them understand the difference?

Answer: Here are effective strategies for distinguishing volume and mass:

  • Concrete examples: Volume = space liquid takes up; Mass = how heavy it is
  • Hands-on activities: Use measuring cups for volume, scales for mass
  • Visual demonstrations: Show same volume of different liquids with different masses

Examples:

  • Volume: A glass holds 250 mL of water
  • Mass: The same 250 mL of water weighs 250 g

For water specifically, volume and mass are numerically equal: 1 L = 1 kg.

Question: My child struggles with converting between liters and milliliters. What strategies can help them?

Answer: Effective strategies for L/mL conversion:

  • Base concept: Remember that 1 L = 1,000 mL
  • Direction matters: L to mL = multiply by 1,000; mL to L = divide by 1,000
  • Decimal movement: Move decimal 3 places left (÷) or right (×)

Practice examples:

  • To convert 2 L to mL: 2 × 1,000 = 2,000 mL
  • To convert 750 mL to L: 750 ÷ 1,000 = 0.75 L

Use real measuring tools to make the concept tangible and visual.

Question: Why does 1 L of water equal 1 kg of mass? Is this always true?

Answer: This relationship is specific to water:

  • Water density: At room temperature, water has a density where 1 L = 1 kg
  • Special property: This makes calculations easy for water
  • Not universal: Other liquids have different densities

Examples:

  • 1 L of water = 1 kg (density = 1 kg/L)
  • 1 L of oil = about 0.9 kg (density = 0.9 kg/L)
  • 1 L of honey = about 1.4 kg (density = 1.4 kg/L)

For this chapter, we assume liquids have the same density as water unless stated otherwise.

Question: What if I have decimals when converting? Like 1.5 L to milliliters?

Answer: When working with decimals, the same rules apply:

  • For L to mL: Multiply by 1,000 (move decimal point 3 places to the right)
  • For mL to L: Divide by 1,000 (move decimal point 3 places to the left)

For 1.5 L to milliliters:

  • 1.5 × 1,000 = 1,500 mL
  • You can think: 1.5 → 15.0 → 150.0 → 1,500.0
  • Move the decimal point 3 places to the right

More examples:

  • 0.25 L = 250 mL (0.250 → 250)
  • 3,500 mL = 3.5 L (3500. → 3.500)

Question: How do I check if my answer is right? Sometimes I'm not sure about my calculations.

Answer: Here are effective ways to check your liquid volume and mass calculations:

  • Unit verification: Did you convert all to the same unit before operations?
  • Reasonableness check: Does your answer make sense?
  • Reverse calculation: Work backwards to verify

Example: If you calculate 2 L of water = 2,000 g:

  • 2 L = 2 kg (using water relationship) ✓
  • 2 kg = 2,000 g (using 1 kg = 1,000 g) ✓
  • Reasonable: 2,000 g is a lot of mass ✓

Always double-check by ensuring your units are consistent!