Question

How many 1/3 cubes does it take to fill a box with a width of 2 2/3 inches length 3 1/3 inches and height 2 1/3

Answer 1

Answer:

560

Step-by-step explanation:

I assume 1/3 is the side length of the cubes.

There's two ways to solve this:

1. Find the volume of the box, then divide by the volume of the cubes.

Or 2. Find the number of cubes per each side length, the find the volume in terms of cubes.

Either way, we need to convert the mixed fractions to improper fractions.

W = 2⅔ = (2×3+2)/3 = 8/3 inches

L = 3⅓ = (3×3+1)/3 = 10/3 inches

H = 2⅓ = (2×3+1)/3 = 7/3 inches

Using the first method, the volume of the box is:

V = (8/3 in) (10/3 in) (7/3 in) = 560/27 in³

The volume of a cube is:

V = (1/3 in)³ = 1/27 in³

So the number of cubes in the box is:

(560/27 in³) / (1/27 in³) = 560

Using the second method, the cubes per each side of the box is:

W = (8/3 in) / (1/3 in) = 8

L = (10/3 in) / (1/3 in) = 10

H = (7/3 in) / (1/3 in) = 7

So the number of cubes is:

8 × 10 × 7 = 560