8th grade Math

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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?

  • 8th grade Math -

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

    576 / 384 = 1.5 inches

  • 8th grade Math -

    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?).

  • 8th grade Math -

    gfh

  • 8th grade Math -

    - square root of 85

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