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Volume is the amount of 3-dimensional space inside a shape. |
If the shape is a prism we can use the area of the end to calculate the volume. We can use the following formula:
| The volume of a prism = Area of base × height |
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EXAMPLE:
The refuse skip in the Figure below is 1.75 m wide and its other dimensions are shown in the diagram alongside it.
Refuse skip
- Calculate the volume of the skip in m3:
Method 1: Using the formula.
To calculate the area, it will need to be split up into smaller pieces.
Skip split up into pieces to calculate its area
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Area A |
= 0.5 × 0.7 m × 0.7 m = 0,245 m2 |
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Area B |
= 2.9 m × 0.7 m = 2.03 m2 |
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Area C |
= 0.5 × 0.9 m × 0.9 m = 0,405 m2 |
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Area D |
= 1.8 m × 0.9 m = 1.62 m2 |
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Area E |
= Area C = 0.405 m2 |
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Total Area of base |
= 0.245 + 2.03 + 0.405 + 1.62 + 0.405 = 4.705 m2 |
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Volume |
= Area of base × height = 4.705 m2 × 1,75 m = 8,23 m3 |
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(Note: The ‘height’ is actually the ‘thickness’ of the prism.) |
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Method 2: Splitting up the volume.
The shape can be split up into different, smaller volumes.
The shape of the skip split up into smaller volumes to calculate its area
Each smaller volume has the same thickness (or width), which is 1.75 m.
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Volume A |
= 0.5 × 0.7 m × 0.7 m × 1.75 m = 0.42875 m3 |
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Volume B |
= 0,7 m × 2,9 m × 1,75 m = 3.5525 m3 |
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Volume C |
= 0.5 × 0.9 m × 0.9 m × 1.75 m = 0.70875 m3 |
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Volume D |
= 0.9 m × 1.8 m × 1.75 m = 2.835 m3 |
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Volume E |
= Volume C = 0.70875 m3 |
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Total volume |
= 8.23375 m3 = 8,23 m3 |
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(Note: The volume of each segment is only rounded off at the end.) |
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Notice that either method can be used to get the same answer. Simply use the method that you are most comfortable with.
- Approximately how many rubbish bags should be able to fit into the above skip if a normal rubbish bag can hold 120 l of refuse? 1 m3 = 1 000 l.
Answer:
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Volume of skip |
= 8.23 m3 x 1 000 = 8 230 l |
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Number of rubbish bags |
= 8 230 l ÷ 120 l = 65,58 bags ≈ 65 bags |
However, the skip will be able to hold a lot more than that number as the bags are usually not totally filled with trash and so more will be able to fit in.