Which expression correctly converts linear dimensions in feet to cubic yards?

Which expression correctly converts linear dimensions in feet to cubic yards?

• A. L x W x H ÷ 27
• B. L x W x H
• C. (L x W) ÷ H
• D. L x W x H x 27

Answer: (A)

To convert linear dimensions in feet to cubic yards, it’s essential to understand the relationship between feet and yards in the context of volume. A yard consists of three feet, which means when dealing with cubic measurements, one cubic yard is equivalent to \(3^3\) or 27 cubic feet. The correct expression for converting cubic feet to cubic yards involves calculating the volume in cubic feet first by multiplying the length (L), width (W), and height (H) in feet. Once this volume is obtained, it must be divided by 27 to convert it into cubic yards. Therefore, the formula L x W x H ÷ 27 accurately reflects this conversion process. Parts of the other expressions do not properly facilitate this conversion. For example, multiplying length, width, and height without any division would simply produce a value in cubic feet rather than cubic yards. Dividing only the area (L x W) by height does not yield a relevant conversion for volume, and multiplying by 27 would incorrectly scale the volume instead of converting it into a smaller measurement. Thus, the expression involving division by 27 clearly aligns with the necessary mathematical transformation from cubic feet to cubic yards.

To convert linear dimensions in feet to cubic yards, it’s essential to understand the relationship between feet and yards in the context of volume. A yard consists of three feet, which means when dealing with cubic measurements, one cubic yard is equivalent to (3^3) or 27 cubic feet.

The correct expression for converting cubic feet to cubic yards involves calculating the volume in cubic feet first by multiplying the length (L), width (W), and height (H) in feet. Once this volume is obtained, it must be divided by 27 to convert it into cubic yards. Therefore, the formula L x W x H ÷ 27 accurately reflects this conversion process.

Parts of the other expressions do not properly facilitate this conversion. For example, multiplying length, width, and height without any division would simply produce a value in cubic feet rather than cubic yards. Dividing only the area (L x W) by height does not yield a relevant conversion for volume, and multiplying by 27 would incorrectly scale the volume instead of converting it into a smaller measurement. Thus, the expression involving division by 27 clearly aligns with the necessary mathematical transformation from cubic feet to cubic yards.