This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Solve Question 1. To represent the data by a pie chart, we first calculate the total number of students and then the central angle for each game. Total number of students = 28 + 8 + 4 + 4 + 1 = 45. The central angle for each game is calculated as: • Cricket: (28)/(45) × 360^ = 224^ • Football: (8)/(45) × 360^ = 64^ • Basketball: (4)/(45) × 360^ = 32^ • Tennis: (4)/(45) × 360^ = 32^ • Hockey: (1)/(45) × 360^ = 8^ To draw the pie chart: • Draw a circle of any convenient radius. • Draw a radius. • Using a protractor, draw sectors with the calculated central angles for each game. • Label each sector with the corresponding game. Step 2: Solve Question 2. To represent the data by a pie chart, we first calculate the total number of students and then the central angle for each language. Total number of students = 36 + 20 + 15 + 30 + 31 + 48 = 180. The central angle for each language is calculated as: • Tamil: (36)/(180) × 360^ = 72^ • Telugu: (20)/(180) × 360^ = 40^ • Kannad: (15)/(180) × 360^ = 30^ • Gujrati: (30)/(180) × 360^ = 60^ • Punjabi: (31)/(180) × 360^ = 62^ • Bangla: (48)/(180) × 360^ = 96^ To draw the pie chart: • Draw a circle of any convenient radius. • Draw a radius. • Using a protractor, draw sectors with the calculated central angles for each language. • Label each sector with the corresponding language. Step 3: Solve Question 3. The pie chart shows the following central angles: Summer (90^), Winter (120^), Rainy (120^). The angle for the unlabeled sector is 360^ - (90^ + 120^ + 120^) = 360^ - 330^ = 30^. a) Which season got the most votes? The season with the largest central angle received the most votes. Both Winter and Rainy seasons have a central angle of 120^. The seasons that got the most votes are Winter and Rainy. b) Find the number of people for each sector if a total of 540 people were surveyed. • Number of people for Summer: (90^)/(360^) × 540 = (1)/(4) × 540 = 135 • Number of people for Winter: (120^)/(360^) × 540 = (1)/(3) × 540 = 180 • Number of people for Rainy: (120^)/(360^) × 540 = (1)/(3) × 540 = 180 • Number of people for the unlabeled sector: (30^)/(360^) × 540 = (1)/(12) × 540 = 45 Step 4: Solve Question 4. To draw a pie chart, we first calculate the total number of people and then the central angle for each food category. Total number of people = 35 + 45 + 12 + 28 = 120. The central angle for each food category is calculated as: • North Indian: (35)/(120) × 360^ = 105^ • South Indian: (45)/(120) × 360^ = 135^ • Chinese: (12)/(120) × 360^ = 36^ • Others: (28)/(120) × 360^ = 84^ To draw the pie chart: • Draw a circle of any convenient radius. • Draw a radius. • Using a protractor, draw sectors with the calculated central angles for each food category. • Label each sector with the corresponding food type. Step 5: Solve Question 5. To draw a pie chart, we use the given percentages to calculate the central angle for each pet category. The central angle for each pet category is calculated as: • Dog: (45)/(100) × 360^ = 162^ • Cat: (25)/(100) × 360^ = 90^ • Parrot: (15)/(100) × 360^ = 54^ • Fish: (10)/(100) × 360^ = 36^ • Others: (5)/(100) × 360^ = 18^ To draw the pie chart: • Draw a circle of any convenient radius. • Draw a radius. • Using a protractor, draw sectors with the calculated central angles for each pet category. • Label each sector with the corresponding pet type. That's 2 down. 3 left today — send the next one.