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Math Help - Geometrical Fish Tank Problem

  1. #1
    Newbie Mars's Avatar
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    Geometrical Fish Tank Problem

    While doing some math practice I encountered this problem:

    "A rectangular fish tank has a base 2 feet wide and 3 feet long. When the tank is partially filled with water, a solid cube with an edge length of 1 foot is placed in the tank. If no overflow of water from the tank is assumed, by how many inches will the level of the water rise when the cube becomes submerged?"

    From what I gathered the area of the base is 6 square feet (obviously) and the volume of the cube is 1 cubic foot. I'm aware that the question says "inches" but I don't believe I have enough information- or that I am scrutinising this question enough to gain such information. Any way to solve this problem?
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  2. #2
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    Re: Geometrical Fish Tank Problem

    dividing the base of cube to 2 feet by 3 feet its height will 1/6 feet so water rise by 2 inches
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  3. #3
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    Re: Geometrical Fish Tank Problem

    Hello, Mars!

    A rectangular fish tank has a base 2 feet wide and 3 feet long. When the tank is
    partially filled with water, a solid cube with an edge length of 1 foot is placed in the tank.
    If no overflow of water from the tank is assumed, by how many inches will the level of
    the water rise when the cube becomes submerged?

    We can talk our way through this problem.

    The original volume of water looks like this:

    Code:
              *-----------*
             /           /|
            /           / |
           /           /  |
          *-----------*   *
          |           |  /
         h|           | /2
          |           |/
          *-----------*
                3
    This block of water has: width 2 feet, length 3 feet, height h feet.
    The volume is: . 2\cdot3\cdot h \:=\:6h\text{ ft}^3


    When the one-foot cube is added, the water looks like this:

    Code:
              *-----------*
             /           /|
            /           / *
           /           / /|
          *-----------* / |
         d|           |/  |
          * - - - - - *   *
          |           |  /
         h|           | /2
          |           |/
          * - - - - - *
                3

    The water has risen to a height of h+d feet.
    This volume is: 6(h+d)\text{ ft}^3
    . . which is 1 cubic foot more than the original volume.

    So we have: . 6(h+d) \:=\:6h + 1 \quad\Rightarrow\quad 6h + 6d\:=\:6h + 1

    . . . . . . . 6d \:=\:1 \quad\Rightarrow\quad d \:=\:\tfrac{1}{6}\text{ ft}


    Therefore, the water rises 2 inches.

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  4. #4
    Newbie Mars's Avatar
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    Re: Geometrical Fish Tank Problem

    Thank you Waqar and Soroban for your help! This question has been solved, and the thread can be closed now.
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