# Volume

Volume is the amount of space taken up by an object or the amount of liquid in a container. The unit of volume used in Primary 3 are millilitres ($\text{mℓ}$) and litres ($\text{ℓ}$).

1. Comparison of volume based on figures
2. Conversion of volume
3. Comparison of volume

## 1. Comparison of volume based on figures

#### Question 1:

Which beaker has the least amount of water?

#### Solution:

Volume of water represents by each marking $=50 \text{ mℓ }$

Volume of water in Beaker A $= 300 \text{ mℓ }$

Volume of water in Beaker B $= 350 \text{ mℓ }$

Volume of water in Beaker C $= 200 \text{ mℓ }$

Volume of water in Beaker D $= 250 \text{ mℓ }$

Beaker C is the one that contains the least amount of water.

#### Question 2:

Which beaker has the most amount of water?

#### Solution:

Volume of water represents by each marking on Beaker A & B $= 10 \text{ mℓ }$

Volume of water in Beaker A $= 60 \text{ mℓ }$

Volume of water in Beaker B $= 80 \text{ mℓ }$

Volume of water represents by each marking on Beaker C & D $= 50 \text{ mℓ }$

Volume of water in Beaker C $= 200 \text{ mℓ }$

Volume of water in Beaker D $= 250 \text{ mℓ }$

Beaker D has the most amount of water

Note: Always take note of the total volume of the container as they can be different for different containers.

## 2. Conversion of volume

To convert volume in litres to millilitres and vice versa, we need to remember that:

$1 \text{ ℓ } = 1000 \text{ mℓ }$

#### Question 1:

$2 \text{ ℓ } =$  __________ $\text{ mℓ }$

#### Solution:

$2 \text{ ℓ } = 2000 \text{ mℓ }$

$2000 \text{ mℓ }$

#### Question 2:

$3 \text{ ℓ } \; 500 \text{ mℓ } =$ __________ $\text{ mℓ }$

#### Solution:

\begin{align} 3 \text{ ℓ } &= 3000 \text{ mℓ } \\[2ex] 3000 \text{ mℓ } + 500 \text{ mℓ } &= 3500 \text{ mℓ } \end{align}

Hence,

\begin{align} 3 \text{ ℓ } \; 500 \text{ mℓ } = 3500 \text{ mℓ } \end{align}

$3500 \text{ mℓ }$

#### Question 3

$5800 \text{ mℓ } =$ __________ $\text{ ℓ }$  __________ $\text{ mℓ }$

#### Solution:

$5000 \text{ mℓ} =5 \text{ ℓ }$

Hence,

$5800 \text{ mℓ} = 5 \text{ ℓ } \;800 \text{ mℓ }$

$5 \text{ ℓ } \; 800 \text{ mℓ }$

## 3. Comparison of volume

#### Question 1:

Arrange the following in ascending order:

$3 \text{ ℓ }$,      $30 \text{ mℓ }$,       $3 \text{ ℓ }\; 3 \text{ mℓ }$,     $300 \text{ mℓ }$

#### Solution:

\begin{align} 3 \text{ ℓ } &= 3000 \text{ mℓ }\\[2ex] 30 \text{ mℓ } &= 30 \text{ mℓ }\\[2ex] 3 \text{ ℓ } \; 3 \text{ mℓ } &= 3003 \text{ mℓ }\\[2ex] 300 \text{ mℓ } &= 300 \text{ mℓ } \end{align}

$30 \text{ mℓ}, \;300 \text{ mℓ}, \;3 \text{ ℓ}, \;3 \text{ ℓ } \;3 \text{ mℓ}$

Note: The final answer must be in the original given quantities.

#### Question 2:

Which of the following has the greatest volume?

1. $6 \text{ ℓ } \; 660 \text{ mℓ }$

2. $6 \text{ ℓ } \;606 \text{ mℓ }$

3. $6 \text{ ℓ } \; 600 \text{ mℓ }$

4. $6 \text{ ℓ } \; 66 \text{ mℓ }$

#### Solution:

No conversion is required as $6 \text{ ℓ }$ are common in all.

By comparing the $\text{ mℓ }$ in all the options, the greatest volume is $6 \text{ ℓ } \; 660 \text{ mℓ }$.

(1) $6 \text{ ℓ } \; 660 \text{ mℓ }$

#### Question 3:

A packet of milk contains $1 \text{ ℓ } \; 125 \text{ mℓ }$ of milk.  A jar of apple juice contains $680 \text{ mℓ }$ of apple juice. A bottle contains $1 \text{ ℓ } \; 250 \text{ mℓ }$ of lemonade juice. Another bottle contains $780 \text{ mℓ }$ of chilli sauce. Which of the following is of the least volume?

1. milk
2. apple juice
4. chilli sauce

#### Solution:

We convert all into millilitres first.
Volume of the packet of milk\begin{align}\\[2ex] &= 1 \text{ ℓ } \; 125 \text{ mℓ }\\[2ex] &= 1125 \text{ mℓ } \end{align}

Volume of the jar of apple juice $= 680 \text{ mℓ }$

Volume of the bottle of lemonade $= 1250 \text{ mℓ }$

Volume of the bottle of chilli sauce $= 780 \text{ mℓ }$

(2) The apple juice is of the least volume.

#### Question 4:

The diagram below shows the amount of water in 3 beakers at first. Sean poured $200 \text{ mℓ}$ of water from Beaker A to Beaker C. He then poured $100 \text{ mℓ }$ of water from Beaker C to Beaker B. Finally, he poured $150 \text{ mℓ }$ of water from Beaker B to Beaker A. Which beaker had the least amount of water in the end?

#### Solution:

Volume of water represents by each marking on the beakers $= 50 \text{ mℓ }$

Volume of water in Beaker A $= 300 \text{ mℓ }$

Volume of water in Beaker B $= 350 \text{ mℓ }$

Volume of water in Beaker C $= 200 \text{ mℓ }$

#### Step 3:Volume of water in Beaker B\begin{align}\\ &= 450 \text{ mℓ } – 150 \text{ mℓ } \\ &= 300 \text{ mℓ } & \text{(Final)} \end{align} Volume of water in Beaker A\begin{align}\\ &= 100 \text{ mℓ } + 150 \text{ mℓ } \\ &= 250 \text{ mℓ } & \text{(Final)} \end{align}

Beaker A has the least amount of water in the end.

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