8.07 Metric units for area and volume
Identify the appropriate unit for measuring the following:
The area of a football field.
The area of a country.
The area of the face of a coin.
The area of an A4 sheet of paper.
Justin uses the conversion equation 1 metre = 100 centimetres to draw two squares with the same area:
Find the area of square A in \text{m}^2.
Find the area of square B in \text{cm}^2.
State the conversion equation from \text{m}^2 to \text{cm}^2.
Convert the following areas to \text{cm}^2:
Convert the following areas to \text{m}^2:
Paul uses the conversion equation 1 kilometre = 1000 metres to draw two squares with the same area:
Find the area of square A in \text{km}^2.
Find the area of square B in \text{m}^2.
State the conversion equation from \text{km}^2 to \text{m}^2.
Convert the following areas to \text{ m}^2:
Convert the following areas to \text{km}^2:
The square shown in the diagram has an area of 1 \, \text{cm}^2:
Find its area in \text{mm}^2.
State the conversion equation from \text{cm}^2 to \text{mm}^2.
Convert the following areas to \text{cm}^2:
Convert the following areas to \text{mm}^2:
Convert the following areas as indicated:
5 \,\text{m}^2 to \text{cm}^2
6 \,\text{km}^2 to \text{m}^2
20\,000 \,\text{cm}^2 to \text{m}^2
1100 \,\text{mm}^2 to \text{cm}^2
12 \,\text{m}^2 to \,\text{cm}^2
11 \,\text{km}^2 to \text{m}^2
7 \,\text{cm}^2 to \,\text{mm}^2
7600 \,\text{cm}^2 to \text{m}^2
27\,000 \,\text{m}^2 to \,\text{km}^2
750 \,\text{mm}^2 to \,\text{cm}^2
10 \,\text{cm}^2 to \,\text{mm}^2
12\,500 \,\text{cm}^2 to \text{m}^2
1\,518\,000 \,\text{m}^2 to \,\text{km}^2
1520 \,\text{mm}^2 to \,\text{cm}^2
The following rectangle has side lengths given in centimetres:
Convert the dimensions of the rectangle into metres.
The following rectangle has side lengths given in millimetres:
The following triangle has dimensions given in millimetres:
Calculate the area of the following rectangles in square centimetres:
A rectangle with side lengths 0.16 \,\text{m} and 0.8 \, \text{m}.
Calculate the area of the following rectangles in square metres:
A rectangle with side lengths 0.018 \, \text{km} and 0.09 \, \text{km}.
Calculate the area of the following rectangles in square kilometres:
A rectangle with side lengths 2900 \,\text{m} and 600 \,\text{m}.
John is tiling a room floor that has a total area of 9 \text{ m}^{2}. The tiles he is using are squares, measuring 25 \text{ cm} by 25 \text{ cm}.
Calculate the area of a single tile in square metres.
How many tiles will John require to cover the entire floor area?
A garden bed measures 430 \text{ cm} by 250 \text{ cm}. A bag of fertiliser covers an area of 2 \text{ m}^{2}.
How many whole bags of fertiliser are needed to cover the total area of the garden bed?
How much area will the left-over fertiliser be able to cover? Give your answer in square metres.
A sand pit set in the corner of a property has dimensions as shown:
Calculate the area of the sandpit in square metres.
A 20 \text{ kg} bag of play sand costs \$7.80, and covers an area of 0.5 \text{ m}^{2} to an appropriate depth.
How much will it cost to buy enough bags of sand to fill this sand pit?
Convert 1 hectare to the following units:
Convert the following areas as indicated:
6 \,\text{ha} to \text{m}^2
2 \,\text{ha} to \text{m}^2
8.11 \,\text{ha} to \text{m}^2
10.7 \,\text{ha} to \text{m}^2
7.25 \,\text{ha} to \text{m}^2
26\,\text{ha} to \text{m}^2
26\,100 \,\text{m}^2 to \text{ha}
200\,000 \,\text{m}^2 to \text{ha}
84\,500 \,\text{m}^2 to \text{ha}
3\,200\,000 \,\text{m}^2 to \text{ha}
9\,750 \,\text{m}^2 to \text{ha}
16\,500\,000 \,\text{m}^2 to \text{ha}
Rectangular farms around Australia were measured and their dimensions are recorded in the table:
Complete the given table by calculating the area of each farm in \text{m}^2.
Which farm has an area of exactly 1 \, \text{ha}?
Which farms have an area of more than 1 \, \text{ha}?
Which farms have an area of less than 1 \, \text{ha}?
| \text{Farm} | \text{Length} \\\ \text{(m)} | \text{Width} \\ \text{(m)} | \text{Area} \\ \text{(m)}^2 |
|---|---|---|---|
| 1 | 300 | 100 | |
| 2 | 350 | 15 | |
| 3 | 100 | 20 | |
| 4 | 350 | 40 | |
| 5 | 100 | 100 |
Identify the appropriate unit for measuring the following:
The volume of a match box.
The volume of an office building.
The volume of swimming pool.
The volume of sim card.
The cube shown in the diagram has a volume of 1 \,\text{cm}^3:
Find its volume in \text{mm}^3.
Convert the following volumes to \text{mm}^3:
Convert the following volumes to \text{cm}^3:
Convert the following volumes to \text{m}^3:
Convert the following as specified:
43\,\text{m}^3 to \text{cm}^3
18\,\text{cm}^3 to \text{mm}^3
12\,000\,000 \,\text{cm}^3 to \text{m}^3
9000 \,\text{mm}^3 to \text{cm}^3
8.97 \,\text{m}^3 to \text{cm}^3
9.77 \,\text{cm}^3 to \text{mm}^3
96\,900 \,\text{cm}^3 to \text{m}^3
92\,200 \,\text{mm}^3 to \text{cm}^3
Find the volume of the following solid in cubic centimetres:
Find the volume of the following solids in cubic millimetres:
