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
Huu hapa ni ukokotozi wa eneo lililotiwa kivuli: Step 1: Tambua taarifa ulizopewa. Radius ya duara ya kwanza (r_1): 10.5 cm Pembe ya katikati ya duara ya kwanza (_1): 83.62^ Radius ya duara ya pili (r_2): 14 cm Pembe ya katikati ya duara ya pili (_2): 60^ Eneo lililotiwa kivuli ni jumla ya sehemu mbili za duara (segments) zinazoundwa na kodi AB. Step 2: Kokotoa eneo la sekta O_1AB. Eneo la sekta hutolewa na fomula A_sekta = ()/(360^) r^2. A_sekta1 = (83.62)/(360) × × (10.5)^2 A_sekta1 = (83.62)/(360) × × 110.25 A_sekta1 ≈ 80.48 cm^2 Step 3: Kokotoa eneo la pembetatu O_1AB. Eneo la pembetatu ya isosceles hutolewa na fomula A_pembetatu = (1)/(2) r^2 (). A_pembetatu1 = (1)/(2) × (10.5)^2 × (83.62^) A_pembetatu1 = (1)/(2) × 110.25 × 0.99373 A_pembetatu1 ≈ 54.78 cm^2 Step 4: Kokotoa eneo la sehemu ya duara (segment) ya kwanza. Eneo la sehemu ya duara ni tofauti kati ya eneo la sekta na eneo la pembetatu. A_sehemu1 = A_sekta1 - A_pembetatu1 A_sehemu1 = 80.48 - 54.78 = 25.70 cm^2 Step 5: Kokotoa eneo la sekta O_2AB. A_sekta2 = (60)/(360) × × (14)^2 A_sekta2 = (1)/(6) × × 196 A_sekta2 ≈ 102.63 cm^2 Step 6: Kokotoa eneo la pembetatu O_2AB. A_pembetatu2 = (1)/(2) × (14)^2 × (60^) A_pembetatu2 = (1)/(2) × 196 × sqrt(3)2 A_pembetatu2 = 49sqrt(3) ≈ 84.87 cm^2 Step 7: Kokotoa eneo la sehemu ya duara (segment) ya pili. A_sehemu2 = A_sekta2 - A_pembetatu2 A_sehemu2 = 102.63 - 84.87 = 17.76 cm^2 Step 8: Kokotoa jumla ya eneo lililotiwa kivuli. Eneo lililotiwa kivuli ni jumla ya maeneo ya sehemu mbili za duara. A_jumla = A_sehemu1 + A_sehemu2 A_jumla = 25.70 + 17.76 = 43.46 cm^2 Eneo lililotiwa kivuli ni 43.46 cm^2. Tuma swali linalofuata 📸