Mathematical equations with geometry.?

Question

Theres a square box that measures 12x12x12 (length, width, height).

There are small cubes that measure 3/4 x 3/4 x 3/4 (length, width, height).

How many small cubes will fit in the big box?

My work led to 2304.

Volume=LxWxH

12^3 = 1728

3/4 (aka: 0.75) .

1728 divided by 0.75 = 2304.

Am I correct?

Answer 1

No, you made one mistake. 1728 should be divided by 0.75³, the volume of one cube.

Another way to solve:

12 inches × 1 cube/(3/4 inch) = 16 cubes

16³ = 4096 cubes

This method doesn't calculate volume.

Answer 2

ok so let me put this in steps

step 1. find the volume of the small cubes

3/4 * 3/4 * 3/4 = .421875 units cubed  dont round as it may affect your answer

step 2. find the volume of the box

12*12*12= 1728

step 3. now divide 1728 by .421875 on your calculator

=4096 exact with no decimals

Now where your mistake was that you did not cube .75 thats why your answer came out the way it did

Answer 3

For each side of 12 we have 12/ (3/4) = 12 *4/3 = 16 smaller sides.

Therefore the cube 12 x 12 x12 have total of

16 x 16 x 16 = 4096 smaller cubes

The answer is 4096 smaller cubes.