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# Radius, Diameter, and Circumference

The **radius** of a circle is a line segment that goes from the **center point to a point on the circle**. Thus, **it goes halfway through the circle.**

The **diameter** of circle is a **line segment** that goes **all the way across a circle through the center point**.

The **circumference** of a circle is the **distance around the outside of the circle**.

The **radius, diameter, and circumference of a circle** always have the **same relationships**. Thus, **if you know one of these, you can calculate the other two**.

**The diameter is always twice as long as the radius**. This makes sense because the diameter is all the way across the circle while the radius is only halfway across.

When circumference is involved, the relationship is a little bit more complex because of the number **(Pi)**.

**Did you know that if you divide the circumference of any circle by its diameter, you will always get the same exact number every time?**

The number you get is called **(Pi)** and is approximately **equal to 3.14**, but the decimal places actually keep going and going.

Computers have calculated millions and even billions of digits to the number , but they haven't been able to find the end of it yet.

**When you use in a problem, typically you can just remember is approximately 3.14.**

**There are three formulas you can use when dealing with the circumference:**

In these formulas,** C = circumference, r = radius, and d = diameter**

**1) Use the formula given below to find the circumference when you know the radius.**

**C = 2x xr**

**2) Use the formula given below to find the circumference when you know the diameter.**

**C = xd**

**3) Use the formula given below to find the diameter when you know the circumference.**

**C = c ÷ **

**Let's take a look at some examples:**

**Example 1**

**Find the radius, diameter, and circumference of each circle.**

Radius = 4 inches **(Remember the radius goes halfway across the circle.)**

The **diameter** is always **twice as long as the radius**.

So, the diameter will be:

**4 x 2 = 8**

The **diameter is 8 inches.**

**For the circumference**, we need to choose a formula.

It's usually better to use the information we are given (instead of the information we figured out ourselves - just in case we made a mistake).

We started with *r* = 4. The first formula **C = 2x xr** has *r* in it, so we will start with that formula and substitute in the information we know.

**C = 2x xr**

**This formula says we must multiply 2 times Pi (3.14) times the radius**

**C = 2x 3.14 xr**

**Then we just need to multiply:**

**C = 25.12 in.**

**Answer: Radius** = 4 in., **diameter** = 8 in., **circumference =25.12 in.**

**Diameter = 6 feet (as shown in the above picture)**

The diameter is always twice as long as the radius.

So, if our diameter is 6 feet, the radius must be half as long as that.

**6 ÷ 2 = 3 **

So the radius is 3 feet long.

**For the circumference**, we need to choose a formula. Remember it's usually better to use the information we are originally given. We started with *d* = 6.

The first formula **C = xd** has *d* in it, so we will start with that formula and substitute in the information we know.

**C = xd**

This formula says we must multiply Pi (3.14) by the diameter.

**C = 3.14x6**

Then we just need to multiply:

**Answer: Radius = 3 ft., **

**C = 18.84 ft.**

**Diameter = 6 ft., **

**Circumference = 18.84 ft.**

We know that the **circumference = 6.28 meters** because we are told this, but we need to find the diameter or radius.

**The formula given below should help us do that:**

d = c ÷

This formula says that to find the diameter, we must take the circumference and divide it by Pi (3.14)

**d = 6.28 ÷ 3.14**

On simplifying we get :

*d* = 2 meters

Now, as we know the diameter, it is easy to find the radius. The diameter is twice as long as the radius, so the radius is half as long as the diameter.

**2 ÷ 2 = 1**

**So, the radius is 1 meter long. **

(And this answer makes sense. If halfway across the circle is 1 meter, all the way across is 2 meters).

**Answer: C = 6.28 m., d ? 2 m., r ? 1 m. **

**Parts of circle**

**1. Radius**

**line segment**that goes from the

**center point to a point on the circle**. Thus, it goes halfway through the circle.

**2. Diameter**

**line segment**that goes

**all the way across a circle through the center point**.

**3. Circumference**

**distance around the outside of the circle**.

Finding radius, diameter, and circumference:

**The diameter is always twice as long as the radius ; d = 2 x r.**

**Important formulas:** **C = 2x xr** , **C = xd** , **d = C ÷ **

**(Pi)** is a **special number** that occurs in circles. Its decimal places keep going and going, but we can use the **approximation 3.14.** So, in calculations, think ? 3.14.