Sophia Marie D. Verdeflor Grade 10-1 STEActivity 13: My Real WorldAnswer the following. Use the rubric provided to rate your work.1. Name 5 objects or cite 5 situations in real life where chords, arcs and central angles of a circle are illustrated. Formulate problems out of these objects or situations, then solve.

a. Charmaine has a circular garden that sheseparates into five equal parts. If the radius ofthe garden is 15 m, what is the length of the arc of each part?360÷5=72°A360°

= l2πr 72°360°

= l2π (15) 15= l

30 π 30π5 =l l = 18.84 m

b. The radius of the pizza measures 20 cm. If the arc of the sliced part of the pizza measures 60°, what is the area of the sector of the pizza?measure of the arc

360 °=¿ 60°360°

=¿ 16A=π r2 A=π (20cm)2 A=400 π cm216 x (400π cm2) = 400 π6 cm2=¿ 200π3 cm2=¿ 209.44 cm2

c. The clock stops at exactly 1:00. The long handpoints to 12 and the short hand points to 1. If theangle formed by 1 o’clock measures 30°, find thefollowing:I. degree measure of an arc formed between12 and 1

II. degree measure of an arc formed between 11 and 2.I. 30°; same as the angle formed by 1 o’clock.II. 360° - 30° = 330°

d. Let say that we divided the sliced orange into 4 different parts with different measurement. Giventhat the sliced parts of the sliced orange measure 120°, 50°, 75° respectively. What is the measure of the last part of the sliced orange?m∠1 + m∠2 + m∠3 + m∠4 = 360°120° + 50° + 75° + m∠4 = 360°

245° -245 m∠4 = 115°

e

e. The length of an arc formed by the Ferris wheelmeasures 10.47 ft. If the circumference of the Ferris wheel is 31.4 ft, what is the degree measure of the arc formed by the Ferris wheel?

A360°

= l2πr A

360°=10.47 ft31.4 ft A=3769.231.4 A = 120°

2. Make a circle graph showing the different school fees that students like you have to pay voluntarily. Ask your school cashier how much you would pay for the following school fees: Parents-Teachers Association, miscellaneous, school paper, Supreme Student Government, and other fees. Explain how you applied your knowledge of central angles and arcs of a circle in preparing the graph.

extra-curricular activities in differ-ent subject area

research fundmembership fees of different clubs

photocopy of paper worksschool projects

School Fees

I applied my knowledge regarding central angles and arcs of the circle byremembering the definitions of each terms so that I would be able to form a circle with correct parts. The circle graph above shows the concept about central angles because the different school fees on the circle graph represent an angle which is known as the central angle because it forms an angle from the center of the circle as its vertex. With regards to arcs, I also applied my knowledge about it because the central angles have its corresponding intercepted arcs, so, basically, If I have central angles in my circle graph, I also have arcs, which is called intercepted arcs.

3. Using the circle graph that you made in number 2, formulate at least two problems involving arcs, central angles, and sectors of a circle, then solve.The different school fees of a typical and ordinary student like me are represented in a circle graph above namely: “School Fees”. Let say that I have Php 5000 budget for different school fees for the whole school year. I spend, Php 2000 for extra-curricular activities in different subject area, Php 1500 for research fund, Php 500 for membership fees of different clubs, Php 200 for photocopy of paper works, and Php 800 for school projects.

a. In the circle graph, what is the measure of the central angle corresponding to each item?By following the formula: (amount of money per school fees ÷ budget for the whole school year-Php 5000) x 360

Extra-curricular activities in different subject area(2000 ÷ 5000) x 360 = 144°

Research fund(1500 ÷ 5000) x 360 = 108°

Membership fees of different clubs(500 ÷ 5000) x 360 = 36°

Photocopy of paper works(200 ÷ 5000) x 360 = 14°

School projects(800 ÷ 5000) x 360 = 58°

b. Suppose the radius of the circle graph is 35 cm. What is the area of each sector in the circle graph? Extra-curricular activities in different subject area

measure of the arc360 °=¿ 144 °360 °

=¿ ( 25 ) (1225 π cm2 ) = 2450π5 cm2=¿ 76935 cm2=¿ 1538.6 cm2 Research fund

measure of the arc360 °

=¿ 108°360°=¿ ( 310 ) (1225π cm2 ) = 3675π10

cm2=11539.510

cm2=¿ 1153.95 cm2

Membership fees of different clubsmeasure of the arc

360 °=¿ 36°360°

=¿ ( 110 ) (1225π cm2 ) = 1225π10cm2=3846.5

10cm2=¿ 384.65 cm2

Photocopy of paper worksmeasure of the arc

360 °=¿ 14 °360°

=¿ ( 7180 ) (1225π cm2 ) = 8575π180cm2=26925.5

180cm2 = 149.58611 cm2

School projects measure of the arc360 °

=¿ 58°360°=¿ ( 29180 ) (1225π cm2 ) = 35525π180

cm2=111548.5180

cm2 = 619.71388 cm2c. With the same value of the radius, how about the measure of the length of the arc of each sector?

Extra-curricular activitiesA360°

= l2πr 144 °360 °

= l2 π (35) 25= l

70 π 140π5 =l 439.65 =l l =87.92 Research fund

A360°

= l2πr 108°360°

= l2π (35) 310= l

70 π 210π10 =l 659.410 =l l =65.94 Membership fees of different clubsA360°

= l2πr 36°360°

= l2π (35) 16= l

70π 70π6 =l 219.86 =l l =36.633 Photocopy of paper worksA360°

= l2πr 14 °360°

= l2π (35) 7180= l

70 π 490 π180=l 1538.6180

=l l =8.548 School projectsA360°

= l2πr 58°360°

= l2π (35) 29180= l

70 π 2030π180=l 6374.2180

=l l =35.412