Water Filter

3 Act Math

Act 1

1. How long will the filter last?
2. Write down a guess.

Act 2

3. What information would be useful to figure this out?
4. Write down some questions you have in your head right now.

Cup Diameter
Cup Height
Initial Flush
Water Consumption

Act 3


5. What would happen if the filter had a capacity of 250 gallons?

Common Core Standards
Understand ratio concepts and use ratio reasoning to solve problems.
Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems.
apply qualitative and quantitative reasoning to solve prediction and comparison of real-world problems involving ratios and rates
solve problems involving the volume of cylinders, cones, and spheres


2 thoughts on “Water Filter

  1. I’m having an issue with this question. When I solve it, I get substantially more weeks than the solution shows. Can you provide the solution?

    1. Hey Shawnquella! Thanks for reaching out. Here is the math I used:


      Looks like I’m getting a lot more days than the answer as well. My guess is that the data I gathered for one week wasn’t always the case during the life of the filter. Also, it’s possible the change filter light on the refrigerator comes on well before the filter is actually finished. In addition, the filter may not last as long as advertised.

      Overall, I bet our math is right, but real life situations don’t always add up the way the should.

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