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 ufumbuzi wa maswali yako: a) Tafuta eneo la duara. Step 1: Tumia fomula ya eneo la duara. Eneo la duara (A) hutolewa na fomula: A = r^2 Ambapo r ni rediasi na ≈ (22)/(7). Step 2: Badilisha thamani za rediasi (r = 7 cm) na . A = (22)/(7) × (7 cm)^2 A = (22)/(7) × 49 cm^2 Step 3: Kokotoa eneo. A = 22 × 7 cm^2 A = 154 cm^2 Eneo la duara ni 154 cm^2. b) Tafuta eneo la sekta ndogo AOB. Step 1: Tumia fomula ya eneo la sekta. Eneo la sekta (A_sekta) hutolewa na fomula: A_sekta = ()/(360^) × r^2 Ambapo ni pembe katikati ya duara, na r^2 ni eneo la duara zima. Kutoka kwenye mchoro, = 60^ na r = 7 cm. Step 2: Badilisha thamani za , r na . A_sekta = (60^)/(360^) × (22)/(7) × (7 cm)^2 A_sekta = (1)/(6) × (22)/(7) × 49 cm^2 Step 3: Kokotoa eneo la sekta ndogo. A_sekta = (1)/(6) × 22 × 7 cm^2 A_sekta = (1)/(6) × 154 cm^2 A_sekta = (77)/(3) cm^2 A_sekta ≈ 25.67 cm^2 Eneo la sekta ndogo AOB ni 25.67 cm^2 (kwa sehemu mbili za desimali). c) Tafuta eneo la sekta kubwa AOB. Step 1: Eneo la sekta kubwa linaweza kupatikana kwa kutoa eneo la sekta ndogo kutoka eneo lote la duara. A_sekta kubwa = A_duara - A_sekta ndogo Step 2: Badilisha thamani za eneo la duara na eneo la sekta ndogo kutoka sehemu (a) na (b). A_sekta kubwa = 154 cm^2 - (77)/(3) cm^2 Step 3: Kokotoa eneo la sekta kubwa. A_sekta kubwa = (154 × 3 - 77)/(3) cm^2 A_sekta kubwa = (462 - 77)/(3) cm^2 A_sekta kubwa = (385)/(3) cm^2 A_sekta kubwa ≈ 128.33 cm^2 Eneo la sekta kubwa AOB ni 128.33 cm^2 (kwa sehemu mbili za desimali). Tuma swali linalofuata 📸