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Math All Around: Garden Hoses and Circumferences

Garden hoses–they’re a common summer sight.

But have you ever wondered whether your hose would reach the flower bed on the other side of the driveway…and wanted to find the answer without having to unwind the hose?

Assuming your hose is wound up in circles, you can use math to find the approximate length of the hose, which would tell you if it’s worth trying to reach that flower bed.

First, measure the diameter of (or the distance across) each of the circles the hose is wound in (they may not all be exactly the same, but we’re looking for a rough idea here).

circle-hose

If the diameter of each circle is about 2 ft, then the circumference of each circle is approximately 3 x 2 ft, or 6 ft, as the circumference equals pi (which we’re rounding to 3 to make the math easier to do in our head) times the diameter.

Circumference = pi x diameter

Circumference = 3 x 2 ft = 6 ft

This means that every time the hose is wound into a circle, it takes about 6 ft of hose.

Now we can count how many times the hose is wound into a circle and multiply that by 6 ft to find the length of hose. If the hose is wound into 10 circles, then we’d know there’s about 10 x 6, or 60 ft, of hose.

Now of course, we’re only approximating the length of the hose. The circles a hose is wound into are likely not all exactly the same size. And we approximated pi to 3, when it’s really a number that begins 3.14 and continues on and on. But often, getting an approximate answer is all we really need. It can give us an idea of whether a hose will extend to that distant flower bed…or let us know about what size hose we’d need to buy to replace it.

Understanding the relationship between the diameter and circumference of a circle applies in more places than you might initially think! In fact, this example was inspired by a man who shared how he uses math on his construction job to estimate the amount of material left on a roll. Remember that math is a tool we can use to help us describe God’s creation and complete the tasks He’s given us to do.


Imagine learning math in connection with real-life applications…all while building a biblical worldview!

Imagine if students really understood algebra and why they needed to learn it.

Well, now they can! Katherine’s newest curriculum covers the core concepts of algebra in a way that leaves students understanding why they’re learning what they’re learning and how it points to the Lord.

 Watch the short video to learn more.

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