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Circle Formulas Vocabulary: Circumference Radius Diameter Pi

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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

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

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

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

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

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Remember that pi is calculated using the ratio of the circumference to the diameter: Another way to say this would be: C÷D = π

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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

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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?

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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

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

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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

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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?

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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

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Area Formula

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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 = πr 2 The area formula works like all the others, just remember your order of operations.

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

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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 5 2 Step 3 - A = 3.14 x 5 2 A = 3.14 x 25 A = 78.5 cm 2 *Note that area is measured in square units

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

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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 6 2 Step 3 - A = 3.14 x 6 2 A = 3.14 x 36 A = 113.04 square feet

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Area Formula What is the area of this circle? 14 inches

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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 7 2 Step 3 - A = 3.14 x 7 2 A = 3.14 x 49 A = 153.86 square inches 14 inches

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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

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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.

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Volume Formula What is the volume of the cylinder?

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Volume Formula Step 1: V =πr 2 h Step 2: V = 3.14 x 7 2 x 12 Step 3: V = 3.14 x 49 x 12 V = 1846.32 cubic inches or 1846.32 in 3

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Volume Formula What is the volume of this cylinder?

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Volume Formula Step 1: V =πr 2 h Step 2: V = 3.14 x 2.25 2 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!

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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.

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