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: Determine the angle swept by the minute hand. A minute hand completes a full circle (360^) in 60 minutes. The angle swept in 1 minute is: (360^)/(60 minutes) = 6^/minute For a stop of 15 minutes, the angle swept () is: = 15 minutes × 6^/minute = 90^ Step 2: Identify the radius of the sector. The length of the minute hand is the radius (r) of the sector. r = 28 cm Step 3: Write down the formula for the area of a sector and substitute the values. The formula for the area of a sector is: A = ()/(360^) r^2 Using = (22)/(7), substitute = 90^ and r = 28 cm: A = (90^)/(360^) × (22)/(7) × (28 cm)^2 Step 4: Calculate the area. A = (1)/(4) × (22)/(7) × 28 cm × 28 cm A = (1)/(4) × 22 × (4 × 28) cm^2 A = 22 × 28 cm^2 A = 616 cm^2 The area swept by the minute hand is 616 cm^2. That's 2 down. 3 left today — send the next one.