Question

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

Answer 1

Answer:

320 cubes

Step-by-step explanation:

3 1/3 inches = 10/3 inches

There are 10 lengths of 1/3 inch in 10/3 inches.

2 2/3 inches = 8/3 inches

There are 8 lengths of 1/3 inch in 8/3 inches.

1 1/3 inches = 4/3 inches

There are 4 lengths of 1/3 inch in 4/3 inches.

In the 3 1/3 inch by 2 2/3 inch by 1 1/3 inch box, you can place 10 by 8 by 4 cubes measuring 1/3 inch on the side.

10 * 8 * 4 = 320

Answer: 320 cubes

Answer 2

It will take 320 cubes of size 1/3 inch  to fill the box a box with a width of 3 1/3 inches, a length of 2 2/3 inches, and a height of 1 1/3 inches

Volume of a cube of side a inch is $\rm a^3\; inch^3$

Length of one side of the cube = 1/3 inch

$\rm Volume\; of \; the \; cube = (1/3)^3 = 1/27 \; inch^3$

$\rm Length\; of \; the \; box = 3 \dfrac{1}{3}\; inches = \dfrac{10}{3}\; inches$

$\rm Width\; of \; the \; box = 2 \dfrac{2}{3}\; inches = \dfrac{8}{3} \; inches$

$\rm Height\; of \; the \; box = 1 \dfrac{1}{3}\; inches = \dfrac{4}{3} \; inches$

$\rm The\; volume \; of \; cuboid\; = \; Length\times Width \times Height\\\\So \; the \; volume \; of\; the\; box = (10/3)\times (8/3) \times (4/3)$

Let there be n be the number of cubes in the box so

Sum of volumes of n cubes = Volume of the box

$\rm n \times (1/27 ) = (10/3)\times (8/3)\times (4/3)\\n \times (1/27) = 320 /27\\n = \bold{320}$

So, It will take 320 cubes of size 1/3 inch  to fill the box a box with a width of 3 1/3 inches, a length of 2 2/3 inches, and a height of 1 1/3 inches.

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