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10.06 Story problems with volume or capacity


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Let's review how to  convert units of volume and capacity  .


Example 1

Convert 6750 cubic centimetres (\text{cm}^3) to litres (\text{L}).

Worked Solution
Create a strategy

Use the conversion 1 \text{ L} = 1000 \text{ cm}^3.

To convert cubic centimetres to litres, divide by 1000.

Apply the idea

Here is 6750 in a place value table.


To divide by 1000 we move each digit to the right three places.


6750 \div 1000 = 6.75

So, 6750 \text{ cm}^3 = 6.75 \text{ L}.

Idea summary

\begin{array}{c} &\text{Volume} & &\text{Capacity} \\ &1 \text{ cm}^3 &= &1 \text{ mL} \\ &1000 \text{ cm}^3 &= &1 \text{ L} \\ &1 \text{ m}^3 &= &1000 \text{ L} \\ &1 \text{ m}^3 &= &1 \text{ kL} \\ \end{array}

Story problems with volume

Let's look at how to solve problems that use volume.

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Example 2

The school is adding new wood chips to the playground. The playground needs 6.5 \text{ m}^3 of wood chips. The wood chips cost \$350 for 1 \text{ m}^3. What is the total cost of the wood chips?

Worked Solution
Create a strategy

Multiply the cost per unit by the volume.

Apply the idea
\displaystyle \text{Cost}\displaystyle =\displaystyle 6.5 \times 350Multiply 6.5 by 350

To multiply a number by a decimal, we first multiply the numbers without the decimal point. We can use a vertical algorithm.

First we multiply 350 by 5 as shown:

\begin{array}{c} && &{}^23 &5 &0 \\ &\times && &6 &5 \\ \hline &&1&7&5&0 \\ \hline \end{array}

Then we multiply 350 by 60:

\begin{array}{c} &&& &{}^33 &5 &0 \\ &\times &&& &6 &5 \\ \hline &&&1&7&5&0 \\ &&2&1&0&0&0 \\ \hline \end{array}

Then we add our two results:

\begin{array}{c} &&& &3 &5 &0 \\ &\times &&& &6 &5 \\ \hline &&&1&7&5&0 \\ &+&2&1&0&0&0 \\ \hline &&2&2&7&5&0 \\ \hline \end{array} But our answer needs to have the same number of decimal places as in the question. 6.5 \times 350 has one decimal place. So the actual answer is 2275.0=2275.

So the cost is \$2275.

Idea summary

We can use vertical algorithms to help solve story problems with volume.

If the units used in the problem are not all the same, we will need to convert between units of volume.

Solve problems with capacity

This video looks at solving problems that involve capacity.

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Example 3

100 \text{ mL} of orange juice, 140 \text{ mL} of pineapple juice and 300 \text{ mL} of soda water are used to make a punch.

Will the entire mixed punch fit into a container with a capacity of 650 \text{ mL}?

Worked Solution
Create a strategy

Add the three numbers and compare the sum to the capacity of the container.

Apply the idea

Add the volumes of the ingredients using a vertical algorithm:\begin{array}{c} &&3&0&0 \\ &&1&4&0 \\ &+&1&0&0\\ \hline &&5&4&0 \\ \hline \end{array}

We have 540 \text{ mL} of punch which is less than 650 \text{ mL}. So the punch will fit into the container.

Idea summary

If we have objects that use the same unit for volume, such as\text{ m}^3, we can add the numbers together to get a total volume. When we need to add the capacity of objects together, we also need to make sure they are using the same unit for capacity.



Connect volume and capacity and their units of measurement

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