Arectangular prism with a volume of 666 cubic units is filled with cubes with side lengths of \dfrac12 2 1 ? start fraction, 1, divided by, 2, end fraction unit. how many \dfrac12 2 1 ? start fraction, 1, divided by, 2, end fraction unit cubes does it take to fill the prism?

Step-by-step explanation:

we know that

The volume of the rectangular prism is equal to

step 1

Find the volume of one cube

The volume of the cube is equal to

where

b is the side length of the cube

we have

substitute

step 2

To find out the number of cubes needed to fill the prism, divide the volume of the rectangular prism by the volume of one cube

so

step-by-step explanation:

12: 00 p.m. to 7: 00 p.m. is a total of 7 hours.

4: 00 p.m. to 7: 00 p.m. is a total of 3 hours.

this means that from 4: 00 p.m to 7: 00 p.m. this represents 3/7 of what was lost from 12: 00 p.m. to 7: 00 p.m.

after knowing this, after doing 11,600 - 6,800 = 4,800

4,800 represents 3/7 of what was lost for 7 hours.

we then divide 4,800 by 3 which gets 1,600.

because we know that 1,600 represents 1/7 of how much water was lost, we just have to multiply by 7, which gets 11,200.   after adding 11,200 to how much water was left at 7: 00 p.m. which was 6,800. 11,200 + 6,800 = 18,000

this means that the pool originally had 18,000 gallons in the pool.

you can also check your work by doing 18,000 - 4(1600), which becomes           1800 - 6400 which gets you 11,600.