Area of a Circle

Area of a Circle

By Courtney Tout

Warm-Up

​S

Open Ended

What do you think about when you hear the word: Area?

We can use the circumference formula when given radius:

C = 2 x pi x r

To help us discover the formula for Area of a Circle​

​

Deriving Area of a Circle Formula

Watch as the circle is transformed into a parallelogram and the area of a circle formula is derived.​

Multiple Choice

We are taking our circle and its' slices and transforming it to form into a parallelogram. One slice is how tall?

• The size of the circumference

• The size of pi

• The size of the diameter

• The size of the radius

Multiple Choice

We are taking our circle and its' slices and transforming it to form into a parallelogram. How long should it be?

• The size of the circumference

• Half the size of the circumference

• T

• The size of the radius

​Using the Area of a Parallelogram formula, lets' determine the area of the parallelogram.

We have transformed our circle, into a parallelogram and relabeled.

​

​base = 1/2 C --> 1/2(2Πr)

height = r

​

1/2 (2​)(Πr) (r) = Π x r x r or Πr²

Area of Parallelogram = b x h​

​

​Area of Circle = Π x r x r

​Area of Circle = Π x r²

Multiple Choice

What is the formula for area of a circle given the radius?

• A = πr
• A = 2πr
• A = πd
• A = πr²

Multiple Select

What all information do you need to know to determine Area of a Circle? [Hint: Select 2 choices]

• Diameter

• Circumference

• Radius

• Pi

Just like with Circumference we set up to solve for Area of a Circle, by plugging things in!

​

Set-It-Up

• We are given a radius of 7 inch

• Plug into our Formula

  • A = Π ​ x 7² which is the same as A = 3.14 x 7 x 7

• Just Multiply to Solve

  • Remember ONLY 2 Numbers at a time - what your decimal place!​

Multiple Select

Set Up to Find the Area [SELECT ALL THAT APPLY]

• $$A=\ 3^2\pi\ \ \ \ or\ \ \ \ A\ =\ 9\pi$$  

• $$A=2\times\pi\times3\times3$$  

• $$A=\pi\times3\times3$$  

• $$A=3.14\times3\times3$$  

Multiple Choice

find the area of the circle below.

• 100 cm
• 225 cm
• 9 cm
• 28.26 cm

Multiple Choice

What is your radius?

•  12 cm

•  10 cm

• 36 cm

• 6 cm

• 144 cm

Multiple Select

Set Up to Find the Area [SELECT ALL THAT APPLY]

• $$A=\pi\times6\times6$$  

• $$A=12\times12\times\pi$$  

• $$A=12^2\pi\$$

  or

  $$A=144\pi$$   

• $$A\ =\ 6^2\pi$$  

  or

  $$A=36\pi$$  

• $$A=3.14\times6\times6$$  

Multiple Choice

What is the area of this circle?

• 163.2
• 15.3
• 124.2
• 113.1

Multiple Choice

A cruise ship has a large, circular window. It has a diameter of 8 meters.

What is the Radius?

• 8 m

• 16 m

• 64 m

• 4 m

Multiple Select

A cruise ship has a large, circular window. It has a diameter of 8 meters.

Set It Up:

• $$A=4^2\pi$$  

• $$A=4^2\times3.14$$  

• $$A=8\pi$$  

• $$A=64\times3.14$$  

• $$A=8\times8\times3.14$$  

Multiple Choice

A cruise ship has a large, circular window. It has a diameter of 8 meters. What is the window's area?

• 31.25 m²

• 29.55 m²

• 30.36 m²

• 50.27 m²