HW: Circumference & Area Wkst #2 (show all algebra) Wednesday, 3/22/17 Write the IC and HW in your planner. IC: Ch. 8 Circles – day 5 HW: Circumference & Area Wkst #2 (show all algebra) Materials Pencil/Grading pen Slate/marker/eraser Math folder Circumference & Area Wkst 0:18 0:19 0:20 0:16 0:15 0:21 0:17 0:23 0:27 0:28 0:26 0:25 0:14 0:24 0:22 0:11 0:03 0:04 0:02 0:01 1:00 End 0:05 0:06 0:10 0:12 0:09 0:08 0:07 0:13 0:29 0:51 0:52 0:50 0:49 0:30 0:48 0:53 0:54 0:59 1:00 0:58 0:57 0:55 0:56 0:46 0:47 0:35 0:45 0:34 0:33 0:31 0:32 0:37 0:36 0:38 0:44 0:42 0:43 0:41 0:39 0:40 1 1 1 1 1

Bellwork red green blue red 1st Pick 2nd Pick 1st Pick 2nd Pick x = x Problem: What is the probability of choosing a red jolly rancher first and then a green? Example: What is the probability of choosing a blue jolly rancher and then a red jolly rancher? red green blue red 1st Pick 2nd Pick 1st Pick 2nd Pick x = x =

Bellwork green blue blue red 1st Pick 2nd Pick 1st Pick 2nd Pick x = x Problem: What is the probability of choosing a green first, putting it back, and then picking a blue? Example: What is the probability of choosing a blue lollipop, putting it back, and then picking a red? green blue blue red 1st Pick 2nd Pick 1st Pick 2nd Pick x = x =

d = 2 cm d = 4 cm d = 10 cm d = 75 cm Circle Approximate Circumference More Precise Circumference Precise! Exact! No rounding! d = 2 cm d = 4 cm d = 10 cm d = 75 cm C  3d C = d C = d C  3(2) C  (3.14)(2) C = (2) C  6 cm C  6.28 cm C = 2 cm C  3d C = d C = d C  3(4) C  (3.14)(4) C = (4) C  12 cm C  12.56 cm C = 4 cm C  3d C = d C = d C  3(10) C  ( )(10) C = (10) C  30 cm C  cm C = 10 cm C  3d C = d C = d C  3(75) C  (3.14)(75) C = (75) C  225 cm C  235.5 cm C = 75 cm

Circumference and Area of Circles Determine the _____________ Choose and write the ____________ ___________________ the variables into the formula _____________ STEPS variables formula Substitute Solve Label

5 in = d 2.5 in = r 15.7 in d = 5 19.625 in² r = 2.5 r = A = ½ C • r Example 2: Circumference = _________ Area = __________ d = 5 19.625 in² r = 2.5 r = A = ½ C • r C =  d A = ½ (15.7)• 2.5 C = 3.14(5) A = 7.85 (2.5) C = 15.7 in A = 19.625 in² 5 in = d 2.5 in = r

Time for Word Problems! 2.5 ft A = ½ C • r d 3.14(5) A = ½ ( )• 2.5 AREA Cover Time for Word Problems! CIRCUMFERENCE Around Example 5: A round table has a radius of 2.5 feet and you need to protect it. (It’s an antique.) How much glass do you need to cover the table to keep it pristine? Area or Circumference? Draw a picture: A = ½ C • r d 3.14(5) A = ½ ( )• 2.5 15.7 2.5 ft = 7.85 (2.5) r = 2.5 19.625 ft² of glass d = 5 d =

Example 8: A round spa has tile that goes around the edge Example 8: A round spa has tile that goes around the edge. How many feet is it to go all the way around the spa if the diameter is 8 feet? Area or Circumference? Draw a picture: C = d C ≈ 3.14(8) C ≈ 25.12 8 ft It is 25.12 feet to go all the way around. d = 8 r = 4 r =

Archimedes 287- 212 B.C.

Archimedes was a mathematician, physicist, engineer, inventor, and astronomer. He is credited with deriving an accurate approximation of the concept of pi.

Archimedes invented a unique way to move water uphill. This technology was also used to get water out of the hull of a ship that had developed a leak or had taken on water.

Archimedes invented a way to light attacking ships on fire using mirrors to focus the energy of the sun.

Archimedes invented a way to lift an attacking ship out of the water to the point that they take on water and then drop it back in to sink.

One theory of the death of Archimedes states that he was killed during the siege of the city he was living in by a invading Roman soldier.

0.4 m 2.512 m 0.5024 m² A = ½ C • r A = ½ (2.512)• 0.4 C =  d Example 3: Circumference = _________ Area = __________ 0.5024 m² A = ½ C • r 0.4 m A = ½ (2.512)• 0.4 C =  d A = 1.256 (0.4) C = 3.14(0.8) C = 2.512 m A ≈ 0.5024 m² r = 0.4 d = 0.8 d =