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A fish tank 24 inches long, 16 inches wide, and 12 inches high is 3/4 full of water. By how many inches will the water level rise if you should add 576 cubic inches of water?

One inch of water in this tank contains 384 cubic inches.

576 / 384 = 1.5 inches

Ms. Sue's insight into this problem was much better than mine and it was cleverly done. If you want to do it the brute force method, which I used, it follows.
Volume of tank = 24x16x12 = 4608 in^3.
3/4 full means it has 4608x(3/4) = 3456 in^3 water in it.
24 x 16 x ??height = 3456 and solve for ?? (the height). That is 3456/(24x16) = 9 inches is the initial height of the water. (That agrees with Ms. Sue's number of 384 for 1" and 384 x 9" = 3456 in^3.
Now we add 576 in^3 to the tank containing 3456 to give a volume of 4032 in^3, then
24 x 16 x ??height = 4032.
height = 4032/(24x16) = 10.5"
So the new height is 10.5", the initial height was 9" so 10.5-9=1.5 inch rise in the water level. (I didn't say it was shorter this way, did I?).

gfh

- square root of 85

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