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
Here's how to find the area of the sector for Q7. Step 1: Identify the given values for the sector. The angle of the sector is = 69^. The radius of the sector is r = 3 cm. We are instructed to use = (22)/(7). Step 2: Apply the formula for the area of a sector. The formula for the area of a sector is A = ()/(360^) r^2. A = (69)/(360) × (22)/(7) × (3 cm)^2 A = (69)/(360) × (22)/(7) × 9 cm^2 Step 3: Simplify the expression. First, simplify the fraction (69)/(360) by dividing both numerator and denominator by their greatest common divisor, which is 3. (69 ÷ 3)/(360 ÷ 3) = (23)/(120) Now substitute this back into the area calculation: A = (23)/(120) × (22)/(7) × 9 cm^2 Multiply the numerators and denominators: A = (23 × 22 × 9)/(120 × 7) cm^2 A = (4554)/(840) cm^2 Simplify the fraction by dividing both numerator and denominator by their greatest common divisor. Both are divisible by 6. (4554 ÷ 6)/(840 ÷ 6) = (759)/(140) cm^2 Step 4: Convert the improper fraction to a mixed number. Divide 759 by 140: 759 ÷ 140 = 5 with a remainder of 59 So, the mixed number is 5 (59)/(140). The area of the sector is 5 (59)/(140) cm^2. What's next?