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Circle Measurements and Calculations

Learn about arc measures, circle properties, and how to find the radius and area of circles. Practice problems included.

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Circle Measurements and Calculations

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  1. F E 80 G O B A 110 O C Have Out: pencil, highlighter, red pen, calculator, HW, GP NB U10D2 Bellwork: Here are some of the new justifications: • arc measure = central  • circle = 360° Determine the following measures. • measure of minor arc AB 2. measure of major arc ACB • measure of minor arc EF 4. measure of major arc EGF 5. Find the radius of a circle with a circumference of 28 in. 6. Find the radius of a circle with an area of 121 m2.

  2. F E 80 G O m AB = m AOB m EF = m EOF m AB = 110 m AB + m ACB = 360 110 + m ACB = 360 m ACB = 250 B A 110 O C 1. measure of minor arc AB 2. measure of major arc ACB (circle = 360) (Arc measure = central ) 3. measure of minor arc EF 4. measure of major arc EGF (circle = 360) m EF + m EGF = 360 (Arc measure = central ) 80  + m EGF = 360 m EF = 80 m EGF = 280

  3. +1 +1 +1 +1 +1 +1 5. Find the radius of a circle with a circumference of 28 in. 6. Find the radius of a circle with an area of 121 m2.

  4. Add to your Circle Vocab Toolkit... m AB O 360 If mAOB = 60 & the radius of O is 5 cm, find the arc measure and the arc length of . m = mAOB length of = length of = m = 60 5 cm 60 B Recall… Arc Measure: Arc Length: A Arc in degrees (same as measure of central … a portion of 360) Length of an arc or distance from one end to the other (measured in ft, cm, in, etc… a portion of circumference)  C Example: (Arc measure = central )

  5. Add to your Circle Vocab Toolkit... Concentric Circles: Circles with the same center.

  6. The figure at the right shows two concentric circles. CS 13 C A a) Which arc has the larger measure: or ? Explain! P B D Both are the same since the measure of the arc is equal to its central angle. Both arcs are intercepted by the SAME central angle! b) Which arc has the greater length? Explain! has the greater length. Arc length is a fraction of the circumference and the outer circle obviously has a larger circumference…therefore the arc would have the greater length even though it is the same portion of its circle. c) How does increasing the length of the radius of a circle affect the arc measure & the arc length? Explain! Increasing the radius INCREASES the arc length but does not have any effect on the arc measure. Arc measure depends on the measure of the central angle, whereas arc length is a piece of the circumference (which is determined by the radius!).

  7. Add to your Circle Vocab Toolkit... m AB r 360 B A O Sector: piece of a circle formed by the two radii of a central angle and the arc between their endpoints on the circle. A SECTOR resembles a slice of a circle. To find the area of a sector, you multiply the portion of the circle by the area of the whole circle.  Asector AOB =

  8. Area of a Sector B 36 10 36 O 10 A Asector AOB =  360 1 1  102  100 = = 10 10 Example Determine the area of sector AOB = 10 u2  31.42 u2

  9. Work on CS 16,18, 19, the worksheet & MCFR #11-22!

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