Circle Formulas Vocabulary Circumference Radius Diameter Pi Circle

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

• 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 x. D 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 = πD Step 2 – substitute numbers for letters where possible: C = 3. 14 x 4 Step 3 – Solve C = 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 = πD Step 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 6 Step 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 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 2 A = πr The area formula works like all the others, just remember your order of operations.

Area Formula Pi times the radius squared A= 2 πr • What is the area of a circle with a radius of 5 cm?

Area Formula • What is the area of a circle with a radius of 5? • Step 1 - A = πr 2 • Step 2 – A = 3. 14 x 52 • Step 3 - A = 3. 14 x 52 A = 3. 14 x 25 A = 78. 5 cm 2 *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 = πr 2 • 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 = πr 2 • 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 = πr 2 h 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 =πr 2 h • Step 2: V = 3. 14 x 72 x 12 • Step 3: V = 3. 14 x 49 x 12 V = 1846. 32 cubic inches or 1846. 32 in 3

Volume Formula • What is the volume of this cylinder?

Volume Formula • Step 1: V =πr 2 h • 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 inches or 58. 21875 in 3 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.