Explain how a cubic yard is equal to 27 cubic feet?

Answer 1

There are in fact 27 cubic feet in a cubic yard. Imagine blocks of size 1 foot by 1 foot by 1 foot (that's 1 cubic foot). Lay 3 in a row, and your row is a yard long. with volume 3 cubic feet. Lay 2 more rows alongside, and you now have 3 rows, giving you a square with 9 blocks, arranged 3 by 3, a yard square, 9 cubic feet. On top of this lay two more identical layers so you have now a block a yard high. Each extra layer is an extra 9 cubic feet, so that's 27 cubic feet, and the whole thing is 1 cubic yard. In summary, if there are 3 feet in a yard, then in a cubic yard there must be 3x3x3 (that is, 3 cubed) cubic feet.

Answer 2

There can be no equivalence.

A cubic foot is a measure of volume in 3-dimensional space, whereas a foot is a measure of length in 1-dimensional space. The two measure different things and, according to the basic rules of dimensional analysis, conversion from one to the other is not valid.

Answer 3

1 yard = 3 feet

(1 yard x 1 yard x 1 yard) = 1 yard3

(3 feet x 3 feet x 3 feet) = 27 feet3

1 cubic yard = 27 cubic feet