Geometry Notes G.11 Circumference/Area of Circles and Sectors Mrs. Grieser Name: ______Date: ______Block: ______Circumference and Arc Length  Circumference: distance around the circle  Arc Length: portion of the circumference

Circumference of a circle = C   d  2 r

Arc Length Corollary In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360o.

Examples: a) Find the circumference of a circle with radius b) Find the radius of a circle with circumference 9 26 Exact Answer: Estimated Answer: Exact Answer: Estimated Answer: (leave in terms of π!)

c) Find the length of d) Find (use (exact and estimated): formula to solve for arc measure)

You try (where possible, give exact and estimated answers)… a) Find the circumference: b) Find the c) Find the radius: length of :

d) Find the circumference: e) Find the radius: f) A skateboard wheel has a diameter of 56 mm. How many revolutions does the wheel make when traveling 3 meters? Geometry Notes G.11 Circumference/Area of Circles and Sectors Mrs. Grieser Page 2 Area of Circles and Sectors

Area of a circle = A   r 2

 Sector of a Circle The region bounded by two radii of the circle and their intercepted arc.

Area of a Sector The ratio of the area of a sector of a circle to the area of the whole circle (πr2) o is equal to the ratio of the measure of the intercepted arc to 360 .

Examples: a) Find the area of a circle with radius 2.5 cm b) Find the diameter of a circle with Exact: Estimated: area = 113.1 cm2

c) Find the areas of the d) Find the area of sectors formed by UTV circle V

You try,,, a) Find the area b) Find the radius c) Find the area of a circle with diameter 11 cm.

d) Find the radius of a circle e) Find the diameter of a circle f) Find the area with area 158.3 yd2. with area 1024π m. of the sectors formed by PQR

g) Find the area of Y. h) Find the i) Find the area of H areas of the sectors formed by ABC