Andrew uses 630 one-inch unit cubes to completely fill the inside of a rectangular box. which could be the dimensions of the box

we have 630 one-inch unit cubes and we want to completely fill the rectangular box (unknown dimensions).

If all the cubes are fitted tightly inside rectangular box without living any space, then box volume would be equal to cubes volume.

There are 630 one-inch unit cubes, so volume of cubes = 630 cubic inches.

Now the volume of rectangular box would also be 630 cubic inches.

We know the formula for volume of rectangular box = length × width × height.

So we need to find any three positive integers whose product is 630.

Out of all given choices, only option A satisfies the condition of factors of 630.

Hence, option A i.e. (7 in x 9 in x 10 in) is the final answer.

Let l = length of larger piece  smaller piece = 5 greater than 1/4 l = 1/4 l + 5  also, the smaller piece = 12  so, put them together:   1/4 l + 5 = 12  and solve for l.  subtract 5 from both sides:   1/4 l = 7  multiply both sides by 4:   l = 28  the length of the bigger piece is 28 meters, and  the total length of the carpet is 28+12 = 40 meters.