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 values and the formula for the area of a sector. The angle of the sector is = 45^. The radius of the circle is r = 3.5 cm. We are asked to use = (22)/(7). The formula for the area of a sector is: Area = ()/(360^) × r^2 Step 2: Substitute the given values into the formula. Area = (45^)/(360^) × (22)/(7) × (3.5 cm)^2 Step 3: Simplify the expression. First, simplify the fraction (45)/(360): (45)/(360) = (1)/(8) Next, calculate (3.5)^2: (3.5)^2 = ((7)/(2))^2 = (49)/(4) Now substitute these back into the area formula: Area = (1)/(8) × (22)/(7) × (49)/(4) cm^2 Step 4: Perform the multiplication. Area = (1 × 22 × 49)/(8 × 7 × 4) cm^2 Area = (1 × (2 × 11) × (7 × 7))/((2 × 4) × 7 × 4) cm^2 Cancel out common factors: Area = (11 × 7)/(4 × 4) cm^2 Area = (77)/(16) cm^2 Step 5: Convert the fraction to a decimal. Area = 4.8125 cm^2 The area of the sector is 4.8125 cm^2. Send me the next one 📸