how many different boxes, all with whole number dimensions and a different size base will have a volume of 8 cubic feet?
2 by 2 by 2
1 by 2 by 4
1 by 1 by 8
Thank you Ms. Sue!!!
You're welcome, Lauren.
To find the number of different boxes with whole number dimensions and a volume of 8 cubic feet, we need to consider all the possible dimensions that can result in a volume of 8.
First, let's list all the possible dimensions that can multiply to give 8:
1 * 8 = 8
2 * 4 = 8
We can see that there are two different combinations that result in a volume of 8 cubic feet: (1, 8) and (2, 4).
Now, we need to consider the size of the base of the boxes. Since the problem states that the base sizes must be different, they cannot have the same dimensions. Therefore, we have two possibilities for the first combination and two possibilities for the second combination:
1. For the combination (1, 8), we can have the base dimensions as (1, 8) or (8, 1). This gives us two unique boxes.
2. For the combination (2, 4), we can have the base dimensions as (2, 4) or (4, 2). This gives us two more unique boxes.
In total, we have four different boxes, each with a different size base and a volume of 8 cubic feet.