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: Identify the given information and angles from the pie chart in Figure 1. Total number of pupils = 180. The angles for each hobby are: Reading: 120^ Sports: 90^ Music: 60^ The angle for Art is not explicitly given, so we calculate it: Angle for Art = 360^ - (120^ + 90^ + 60^) = 360^ - 270^ = 90^. Step 2: Determine the number of pupils for each hobby. The number of pupils for a hobby is calculated as Angle for hobby360^ × Total number of pupils. a) i) Reading: Number of pupils = (120^)/(360^) × 180 = (1)/(3) × 180 = 60 pupils ii) Sports: Number of pupils = (90^)/(360^) × 180 = (1)/(4) × 180 = 45 pupils iii) Music: Number of pupils = (60^)/(360^) × 180 = (1)/(6) × 180 = 30 pupils iv) Art: Number of pupils = (90^)/(360^) × 180 = (1)/(4) × 180 = 45 pupils Step 3: Calculate the percentage of pupils whose hobby is each category. The percentage for a hobby is calculated as Angle for hobby360^ × 100\%. b) i) Reading: Percentage = (120^)/(360^) × 100\% = (1)/(3) × 100\% = 33.33\% (rounded to two decimal places) ii) Sports: Percentage = (90^)/(360^) × 100\% = (1)/(4) × 100\% = 25\% iii) Music: Percentage = (60^)/(360^) × 100\% = (1)/(6) × 100\% = 16.67\% (rounded to two decimal places) iv) Art: Percentage = (90^)/(360^) × 100\% = (1)/(4) × 100\% = 25\% 3 done, 2 left today. You're making progress.