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
Welcome back — been a while! Let's pick up where you left off. The question asks to find the area and perimeter of a sector of a circle with a radius of 21 cm and an angle of 120^. Given: Radius, r = 21 cm Angle, = 120^ Step 1: Calculate the area of the sector. The formula for the area of a sector is A = ()/(360^) × r^2. A = (120^)/(360^) × (22)/(7) × (21 cm)^2 A = (1)/(3) × (22)/(7) × 441 cm^2 A = (1)/(3) × 22 × 63 cm^2 A = 22 × 21 cm^2 A = 462 cm^2 The area of the sector is 462 cm^2. Step 2: Calculate the perimeter of the sector. The formula for the perimeter of a sector is P = ()/(360^) × 2 r + 2r. P = (120^)/(360^) × 2 × (22)/(7) × 21 cm + 2 × 21 cm P = (1)/(3) × 2 × 22 × 3 cm + 42 cm P = 44 cm + 42 cm P = 86 cm The perimeter of the sector is 86 cm. Send me the next one 📸