G

eometry:

Look at my head! It’s almost a perfect circle!

Finding the Circumference and Area of Circles

In this lesson, you will learn the formulas for: 

Circumference

around a circle.

– the distance Area 

Area

– the number of square units a circle contains.

A few more terms you need to know…

Radius

to the center of a circle from any edge.

– a line that goes

Diameter

– a line that goes all the way across a circle through its center.

Pi

or

π

– a number (3.14) that we use to figure out the circumference and area of circles.

So how do we find the circumference of a Grubby Dub’s Pizza?

Diameter = 18 in First, we need to know the diameter of the pizza.

And then we use the following formula:

𝐶𝑖𝑟𝑐𝑢𝑚𝑓𝑒𝑟𝑒𝑛𝑐𝑒 = 𝜋 × 𝑑

In the big leagues, we write that formula like this:

𝑪 = 𝝅𝒅

Diameter = 18 inches

That doesn’t seem bad, but what if you’re only given the radius?

𝑪 = 𝝅𝒅

C = 3.14 × 18 C ≈ 56.5 in That’s a great question! Check this out!

Radius = 12 in Here, we’re given a radius, but we need a diameter to find the circumference of the dart board.

So, what should we do to this radius?

If you said we need to “double” it, you’re right!

That’s right! Someone’s on top of their game today.

Isn’t doubling like multiplying by 2?

It’s a gift.

Radius = 12 in C = 2 × 3.14 × 12 C ≈ 75.4 in

𝑪 = 𝝅𝒅

or

𝑪 = 𝟐𝝅𝒓

We’ll use this formula here!

Now, let’s take a look at finding the

area

of a circle!

Let’s find the area of this stained glass window!

𝐴𝑟𝑒𝑎 = 𝜋 × 𝑟

2 or

𝐴 = 𝜋𝑟

2 𝐴 = 3.14 × (2) 2 Radius = 2 ft Remember!

You MUST always follow order of operations and simplify exponents FIRST!

𝐴 = 3.14 × 4 𝐴 ≈ 12.6 ft 2

Do you think you could find the area of say… my face?

That’s a little awkward, but I suppose we could!

Sweet!

How do we do this?

First, we need to measure the width of your face.

It looks like the diameter of your face is about 13 inches.

Is that good?

Well…umm… Remember! To find the area, of a circle we need the radius.

𝐴 = 𝜋𝑟 2 𝐴 = 3.14 × (6.5) 2 So, divide the diameter by 2!

13 ÷ 2 = 6.5 in r = 6.5 in 𝐴 = 3.14 × 42.25

𝐴 ≈ 132.7 in 2 That’s quite a dome you have there!

1.

Find the circumference for number’s 1 and 2.

Let’s practice!

Find the area for number’s 3 and 4.

Round all answers to the nearest tenth.

3.

11 ft 7 in A ≈ 38.5 in 2 C ≈ 69.1 ft

2.

4.

12 km 7 m C ≈ 22 m A ≈ 452.2 km 2