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 .

A= ( 3 ) 2 =9

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.

Customary Units Metric Units
1  yd 2 =9  ft 2 1  m 2 =10,000  cm 2
1  ft 2 =144  in 2 1  cm 2 =100  mm 2

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 .

V=( 12 )( 12 )( 12 ) =1,728

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.

Customary Units Metric Units
1  yd 3 =27  ft 3 1  m 3 =1 ,000,000  cm 3
1  ft 3 =1,728  in 3 1  cm 3 =1,000  mm 3

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 mL1 g )

Note:

A length is measured in units, area is measured in square units ( unit×unit= unit 2 ) , and volume is measured in cubic units ( unit×unit×unit= unit 3 ) .