CIRCUMFERENCE OF CIRCLES

• What is the definition of a circle?

• A flat shape whose points are all the same distance away from the center

• This distance from the center to the edge is called the radius

• What is a diameter of a circle?

• How are the radius and diameter of a circle related?

• A line that goes through the center of a circle and connects two points on the edge

• A diameter is two radii put together. So the diameter is twice the length of the radius.

• Diameter = 2×radius

• What is the diameter of this circle?

• What is the radius of this circle?

• Diameter = 2×radius d = 2×4 meters d = 8 meters

• Diameter = 2×radius 18 meters = 2 × r÷ 2 ÷ 29 meters = r

• What is the circumference of a circle?

• The distance around the outside of a circle.

• This is a special name for the perimeter of a circle.

• What is π? • π (pronounced pi) is the ratio of any circle’s circumference to its diameter.

• π is an irrational number, which means it is a decimal that never repeats.

• Sometimes you can leave π in your answer. If you need to estimate, substitute 3.14 or for π.

• How do we calculate the circumference of a circle?

• If we know the radius of the circle, use the formula Circumference = 2×π×radius

• If we know the diameter of the circle, use the formulaCircumference = π×diameter

• These are really the same formula! If you multiply 2×radius you get the diameter.

• What is the circumference of this circle?

• Since we know radius = 3 cm, use the formulaCircumference = 2×π×radius

• C = 2×π×3 cm C = 6π cm

• Estimate using π = 3.14: C = 6×3.14 cm C = 18.84 cm

• What is the circumference of this circle?

• Since we know diameter = 4 cm, use the formula Circumference = π×diameter

• C = π × 4 cm C = 4π cm

• Estimate using π = 3.14: C = 4×3.14 cm C = 12.56 cm

Direct Station• We will use the whiteboards to practice radius, diameter,

and circumference problems

Collaborative Station: Estimating• For each problem, you and your partner(s) will be given a

circle with either its radius or diameter given.• Each partner will guess what the circumference will be.

Write this down!• Once everyone has guessed, calculate the actual

circumference and see who was closer.• Here is an example of what you should write

on your paper:• Think about the formula when you make

your guess! You should be able to getaccurate guesses very quickly

Independent Station• Continue ST Math’s unit on area and perimeter