In this post, we are going to determine plausible sizes of a Super Mario pipe. Let’s look at the curriculum expectations for grade 8 math:

- determine, through investigation using a variety of tools and strategies (e.g., generalizing from the volume relationship for right prisms, and verifying using the capacity of thin-walled cylindrical containers), the relationship between the area of the base and height and the volume of a cylinder, and generalize to develop the formula (i.e.,Volume = area of base x height);
- determine, through investigation using concrete materials, the surface area of a cylinder (Sample problem: Use the label and the plastic lid from a cylindrical container to help determine its surface area.);
- solve problems involving the surface area and the volume of cylinders, using a variety of strategies (Sample problem: Compare the volumes of the two cylinders that can be created by taping the top and bottom, or the other two sides, of a standard sheet of paper.).

For the purposes of this task, we will use Super Mario 1. Familiarize yourself with it below:

Although the graphics have improved, the character sizes have not changed. Mario is estimated to be 155 cm tall (5’11”) and approximately 200 pounds.

**1) Estimate the height and weight of the remaining characters.**

**2) Based on the data above, estimate the dimensions of the pipe pictured here:**

**3) Considering Bowser must travel through these worlds, determine the volume of these pipes. How much space is there inside to allow Nintendo characters to safely travel through them.**

**4) Looks like the pipes need some work. How much paint is needed to re-coat this pipe once?**

**5) How tall is the flagpole?**

Great job! We can work in proportions here too. An interesting questions: If Mario weighs 200lbs how much volume does he take up?

Perfect extension!

Or if you want to tie it to science: If the pipe were full of water, how much water would Mario displace when he jumped in?