PLEASE HELP I NEED THIS I AM GIVING LOTS OF POINTS How many 1/3 inch cubes does it take to fill a box with width 2 2/3 inches, length 3 1/3 inches, and height 2 1/3 inches?

Work Shown:

Let's find out how many smaller cubes are needed to go along the 2 & 2/3 inch side length of the bigger box.

First convert to an improper fraction

2 & 2/3 = 2 + 2/3 = 6/3 + 2/3 = 8/3

Divide this over the side length of the small cube to get

8/3 divided by 1/3 = (8/3)*(3/1) = 24/3 = 8

So we need exactly 8 small cubes along the 2 & 2/3 inch side length.

Let A = 8 so we can use this later.

Repeat the same steps for the 3 & 1/3 inch side length

3 & 1/3 = 3 + 1/3 = 9/3 + 1/3 = 10/3

10/3 divided by 1/3 = (10/3)*(3/1) = 30/3 = 10

We need 10 cubes along the 3 & 1/3 inch side length.

Let B = 10.

Repeat for the 2 & 1/3 inch side length

2 & 1/3 = 2 + 1/3 = 6 + 1/3 = 7/3

7/3 divided by 1/3 = (7/3)*(3/1) = 21/3 = 7

We need 7 cubes along the 2 & 1/3 inch side length

Let C = 7

Multiply out the values of A,B,C to get

A*B*C = 8*10*7 = 560

This means we need 560 cubes that are each 1/3 of an inch along the the side to fill up a box that has dimensions of 2 & 2/3 inches by 3 & 1/3 inches by 2 & 1/3 inches.

the perimeter is increased by a factor of 2