Circle Formulas

• Vocabulary:

• Circumference• Radius• Diameter• Pi

Circle Formulas

• Circumference– the distance around the outside of a circle

• Radius– the distance from the center of a circle to any point on the

outside • Diameter

– the distance from one side of the circle to another passing through the center

• Pi– a numerical constant approximately equal to 3.14

– represented by this symbol: π

• If the diameter of a circle is 12, what is the radius?

• If the diameter of a circle is 12, what is the radius?

• The radius will always be ½ of the diameter, so the radius of the circle in this case is 6.

• If the radius of a circle is 1.5, what is the diameter of the circle?

• If the radius of a circle is 1.5, what is the diameter of the circle?

• Diameter is always twice the radius, so the diameter of this circle would be 3.

• Remember that pi is calculated using the ratio of the circumference to the diameter:

• Another way to say this would be:C÷D = π

€

circumference

diameter= π

• Another way to say this would be:C÷D = π

• Using your algebra “juggling” skills, it should be clear why the formula to find the circumference of a circle is π times the diameter or:πD

• C÷D = π xD xD C = πD

Circumference Formula

The circumference formula works just like the other geometric formulas you’ve learned – the only new thing is π, which, for the GED, is always equal to 3.14

What is the circumference of a circle with a diameter of 4?

Circumference Formula

What is the circumference of a circle with a diameter of 4?

Step 1 – Write the formula:C = πDStep 2 – substitute numbers for letters where

possible:C = 3.14 x 4Step 3 – SolveC = 12.56

Circumference Formula

• What is the circumference of a circle with a radius of 3 inches?

Circumference Formula

• What is the circumference of a circle with a radius of 3 inches?

Step 1 - C = πDStep 2 – we need the diameter to go in place of

the variable “D” – if the radius is 3, then the diameter is 6, so:

C = 3.14 x 6Step 3 – C = 18.84

Circumference Formula

• If necessary, you should also be able to find the diameter of a circle if you’re given the circumference.

• What is the diameter of a circle with a circumference of 25.12?

Circumference Formula

• What is the diameter of a circle with a circumference of 25.12?

• Step 1 - C = πD• Step 2 – 25.12 = 3.14 x D• Step 3 – 25.12 = 3.14 x D

÷3.14 ÷3.14

8 = D

Area Formula

Area Formula

• The formula to find the area of a circle, or the number of square units that would fit inside it, is:Pi times the radius squared

A = πr2

The area formula works like all the others, just remember your order of operations.

Area Formula

Pi times the radius squared

A = πr2

• What is the area of a circle with a radius of 5cm?

Area Formula

• What is the area of a circle with a radius of 5?• Step 1 - A = πr2

• Step 2 – A = 3.14 x 52

• Step 3 - A = 3.14 x 52

A = 3.14 x 25 A = 78.5 cm2

*Note that area is measured in square units

Area Formula

• What is the area of a circle with a diameter of 12 feet?

Area Formula

– What is the area of a circle with a diameter of 12 feet?

• Step 1 - A = πr2

• Step 2 – We need the radius, which is half of the diameter, so:

A = 3.14 x 62

• Step 3 - A = 3.14 x 62

A = 3.14 x 36 A = 113.04 square feet

Area Formula

• What is the area of this circle?

14 inches

Area Formula

• What is the area of this circle?

• Step 1 - A = πr2

• Step 2 – We need the radius, which is half of the diameter, so:

A = 3.14 x 72

• Step 3 - A = 3.14 x 72

A = 3.14 x 49 A = 153.86 square inches

14 inches

Volume Formula

• A cylinder is a 3 dimensional container with the top and bottom circular. It’s another word for a tube shape. On the GED, you might need to calculate the volume of a can or a barrel.

• Volume is measured in cubic units

Volume Formula

• The formula for volume of a cylinder is: radius

•V = πr2h height

Notice that it’s the area formula times the height of the cylinder.

Volume Formula

• What is the volume of the cylinder?

Volume Formula

• Step 1: V =πr2h• Step 2: V = 3.14 x 72 x 12• Step 3: V = 3.14 x 49 x 12

V = 1846.32 cubic inchesor 1846.32 in3

Volume Formula• What is the volume of this cylinder?

Volume Formula

• Step 1: V =πr2h• Step 2: V = 3.14 x 2.252 x 11.5• Step 3: V = 3.14 x 5.0625 x 11.5

V = 58.21875 cubic inchesor 58.21875 in3

If you get a problem like this one on the GED, it’s pretty safe to say it will be on the calculator-allowed section!

Circle Formulas

• Fill out the worksheets on pages 158 through the top of page 161 in the book.Check your answers using the key on BB.