How do you solve R in C 2pir?

Cracking the Circle Code: Finding the Radius When You Know the Circumference

Circles! They’re everywhere, right? From the wheels on your car to the dinner plate in your cupboard, these perfect shapes pop up in all sorts of places. And understanding them, even just a little, can be surprisingly useful. One of the most basic things to know about a circle is its circumference – that’s just the distance all the way around the edge. But what if you know the circumference and need to find the radius? Don’t sweat it; it’s easier than you think.

The Magic Formula: C = 2πr

Okay, let’s get a little math-y, but I promise it won’t hurt. The circumference (we call it “C”) is always linked to the radius (that’s “r”) by a special number called pi (π). Pi is just a little over 3, about 3.14159 to be more precise, and it shows up whenever you’re dealing with circles. The formula that ties it all together is: C = 2πr. Think of it as the circle’s secret handshake.

Unlocking the Radius: r = C / (2π)

So, how do we flip that formula around to find the radius? Well, we need to get “r” all by itself on one side of the equals sign. Right now, it’s being multiplied by 2π. To undo that, we just divide both sides of the equation by 2π. It’s like unwrapping a present!

That gives us: r = C / (2π)

Boom! That’s it. That’s the formula you need to find the radius when you know the circumference. Seriously, it’s that simple.

Let’s Do This: A Step-by-Step Walkthrough

Ready to put it into action? Here’s how it works:

Example Time:

Imagine you’re building a circular garden, and you want the fence around it to be 50 feet long (that’s the circumference). How big should the garden be across (the diameter, which is twice the radius)?

r = 50 feet / (2π)


r = 50 feet / (2 * 3.14159)


r ≈ 7.96 feet

So, the radius of your garden should be about 7.96 feet. Double that, and you get the diameter: roughly 15.92 feet across. Perfect for those prize-winning roses!

Why Bother? Real-World Uses

Okay, so maybe you’re not building a garden. Why should you care about this stuff? Well, knowing how to find the radius from the circumference pops up in all sorts of unexpected places:

• Construction: Ever wonder how they build those giant circular arenas? This formula is part of it.
• Engineering: Designing gears, pulleys, anything round… it all comes back to circles.
• DIY Projects: I used this once to figure out how much edging I needed for a circular patio. Saved me a trip to the hardware store!

A Quick Word About Pi

Pi is one of those numbers that’s just… weird. It goes on forever without repeating. People have calculated it to trillions of digits, just for fun! You can get by with 3.14 or 22/7 for most things, but if you need super-precise answers, use the pi button on your calculator.

The Circle, Unlocked

So, there you have it. Finding the radius when you know the circumference is a piece of cake (or pie, should I say?). It’s a simple formula with a surprising number of uses. And who knows, maybe it’ll come in handy someday when you’re designing your own circular masterpiece!