Convert Units of Area and Volume

The objective of the lesson is to convert units of measure between dimensions including area and volume.

Area:

The area is measured in square units (unit 2).

Example 1:

Convert one square yard to square feet.

A square yard is a square with a side length of one yard.

We know that, 1 yard = 3 feet.

So, 1 square yard is a square with side length 3 feet.

You can use the formula for the area of a square, A = s 2 , to convert square units.

Since 1 yard = 3 feet, substitute s by 3.

So, 1 square yard is equal to 9 square feet.

Common conversions for Square Units

The table gives several common measurement conversions for square units.

Volume

The volume is measured in cubic units (unit 3).

Example 2:

Convert one cubic foot to cubic inches.

A cubic foot is a cube with a side length of one foot.

We know that, 1 foot = 12 inches.

So, 1 cubic foot is a cube with side length 12 inches.

You can use the formula for the volume of a prism, V = bwh , to convert cubic units.

Since 1 foot = 12 inches, replace b , w , and h with 12.

So, 1 cubic foot is equal to 1,728 cubic inches.

Common conversions for cubic units

The table gives several common measurement conversions for cubic units.

The metric system also relates length, mass, and capacity.

1 milliliter has the same volume as 1 cubic centimeter. (1 mL = 1 cc)

1 milliliter of water is approximately 1 gram. (1 mL \approx; 1 g)

Note:

A length is measured in units , area is measured in square units , and volume is measured in cubic units .