A cube has side lengths of 25 cm long. If Sam has 16 of these cubes, what total volume would the cubes occupy written as a power of 2?
The total volume is 2____ cm3
The formula to calculate the volume of a cube is V = s^3, where s is the length of a side.
In this case, the side length of each cube is 25 cm long, so the volume of each cube is 25^3 = 15,625 cm^3.
Since Sam has 16 of these cubes, the total volume of all the cubes is 16 * 15,625 = 250,000 cm^3.
To write this total volume as a power of 2, we need to find the largest power of 2 that is smaller than 250,000. We can do this by repeatedly dividing 250,000 by 2 until we reach a value less than 2.
250,000 divided by 2 is 125,000
125,000 divided by 2 is 62,500
62,500 divided by 2 is 31,250
31,250 divided by 2 is 15,625
So the largest power of 2 that is smaller than 250,000 is 2^15 = 32,768.
Therefore, the total volume of the cubes can be written as a power of 2 as 2^15 cm^3.