Area Conversion

Similar to the previous conversions, the conversion table and conversion factor are also important in area conversion. Observe that most units of area is using the same units of length but “squared”. These are called square units.


Here are the steps:


Step #1: Identify the units used.

Step #2: Determine the relationship between the units.

Step #3: Determine the conversion factor (in fraction form).

The denominator should have the same unit as the original measurement.

Square the conversion factor.

Step #4: Multiply the original measurement by the conversion factor.


Example 1.1
 43.06 `ft^2`
Explanation:

Step #1: Determine the units used.

The units are square meters `(m^2)` and square feet `(ft^2)`.


Step #2: Determine the relationship between the units.

1 ft = 30.48 cm = 0.3048 m


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

Square the conversion factor.

The original measurement is in square meters.

So, the denominator of the conversion ratio should be in square meters.

The conversion factor is `((1 ft) / (0.3048 m))^2`


Step #4: Multiply the original measurement by the conversion factor.

`4 m^2 `X `((1 ft) / (0.3048 m ))^2=43.06 ft^2`

Example 1.2
 2 `cm^2`
Explanation:

Step #1: Determine the units used.

The units are square millimeters (`mm^2`) and square centimeters (`cm^2`).


Step #2: Determine the relationship between the units.

1 cm = 10 mm


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

Square the conversion factor.

The original measurement is in square millimeters.

So, the denominator of the conversion ratio should be in square millimeters.

The conversion factor is `((1 cm) / (10 mm))^2`


Step #4: Multiply the original measurement by the conversion factor.

`200 mm^2 `X `((1 cm) / (10 mm ))^2=2 cm^2`


 Volume (Space) Conversion


Similar to the area conversion, the method for volume (space) conversion is nothing different. Most units of volume (space) is using the same units of length but “cube”. These are called cubic units.


Here are the steps:


Step #1: Identify the units used.

Step #2: Determine the relationship between the units.

Step #3: Determine the conversion factor (in fraction form).

The denominator should have the same unit as the original measurement.

Cube the conversion factor.

Step #4: Multiply the original measurement by the conversion factor.


Example 2.1
 0.005 `m^3`
Explanation:

Step #1: Determine the units used.

The units are cubic centimeters `(cm^3)` and cubic meters `(m^3)`.


Step #2: Determine the relationship between the units.

1 m = 100 cm


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

Cube the conversion factor.

The original measurement is in cubic centimeters.

So, the denominator of the conversion ratio should be in cubic centimeters.

The conversion factor is `((1 m) / (100 cm))^3`


Step #4: Multiply the original measurement by the conversion factor.

`5000 cm^3 `x `((1 m) / (100 cm ))^3 =0.005 m^3`

Therefore, 5000 `cm^3` = 0.005 `m^2`

Example 2.2
 5184 `text(in)^3`
Explanation:

Step #1: Determine the units used.

The units are cubic feet `(ft^3)` and cubic inches `(text(in)^3)`.


Step #2: Determine the relationship between the units.

1 ft = 12 in


Step #3: Determine the conversion factor (in fraction form).

Take note that the denominator should have the same unit as the original measurement.

Cube the conversion factor.

The original measurement is in cubic centimeters.

So, the denominator of the conversion ratio should be in cubic centimeters.

The conversion factor is `((12 text(in)) / (1 ft))^3`


Step #4: Multiply the original measurement by the conversion factor.

`3 ft^3 `X `((12 text(in)) / (1 ft))^3 =5184 text(in)^3`

Therefore, 3 `ft^3` = 5184 `text(in)^3`






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