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Calculate the area and circum. farance of figure below.

Mathematics

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Ili kutatua swali hili, tutachukulia kuwa umbo lililopewa ni sekta ya duara. Pia, tutachukulia kuwa '500' iliyoandikwa kwenye picha inamaanisha pembe ya 50∘50^\circ iliyoondolewa kutoka kwenye duara kamili, kwani 500∘500^\circ haingewezekana kwa muktadha huu.

  1. Tambua vipimo vilivyopewa na kokotoa pembe ya sekta iliyobaki.

    Radius ya duara r=7 mr = 7 \text{ m}.
    Pembe ya sehemu iliyoondolewa θremoved=50∘\theta_{\text{removed}} = 50^\circ.
    Pembe ya sekta iliyobaki θremaining=360∘−θremoved\theta_{\text{remaining}} = 360^\circ - \theta_{\text{removed}}.

    θremaining=360∘−50∘=310∘\theta_{\text{remaining}} = 360^\circ - 50^\circ = 310^\circ
  2. Kokotoa eneo la umbo (sekta iliyobaki).

    Fomula ya eneo la sekta ni A=θ360∘×πr2A = \frac{\theta}{360^\circ} \times \pi r^2.

    A=310∘360∘×π(7 m)2A = \frac{310^\circ}{360^\circ} \times \pi (7 \text{ m})^2 A=3136×49π m2A = \frac{31}{36} \times 49\pi \text{ m}^2 A=151936π m2A = \frac{1519}{36}\pi \text{ m}^2

    Kutumia π≈3.14159\pi \approx 3.14159:

    A≈151936×3.14159A \approx \frac{1519}{36} \times 3.14159 A≈132.59 m2A \approx 132.59 \text{ m}^2

    Eneo la umbo ni 132.59 m2\boxed{\text{132.59 m}^2}.

  3. Kokotoa urefu wa upinde (arc length) wa sekta iliyobaki.

    Fomula ya urefu wa upinde ni L=θ360∘×2πrL = \frac{\theta}{360^\circ} \times 2\pi r.

    L=310∘360∘×2π(7 m)L = \frac{310^\circ}{360^\circ} \times 2\pi (7 \text{ m}) L=3136×14π mL = \frac{31}{36} \times 14\pi \text{ m} L=21718π mL = \frac{217}{18}\pi \text{ m}

    Kutumia π≈3.14159\pi \approx 3.14159:

    L≈21718×3.14159L \approx \frac{217}{18} \times 3.14159 L≈37.87 mL \approx 37.87 \text{ m}
  4. Kokotoa perimita (circumference) ya umbo.

    Perimita ya umbo ni jumla ya urefu wa upinde na radii mbili za moja kwa moja.
    Perimita P=Urefu wa Upinde+r+rP = \text{Urefu wa Upinde} + r + r

    P=21718π m+7 m+7 mP = \frac{217}{18}\pi \text{ m} + 7 \text{ m} + 7 \text{ m} P=21718π m+14 mP = \frac{217}{18}\pi \text{ m} + 14 \text{ m} P≈37.87 m+14 mP \approx 37.87 \text{ m} + 14 \text{ m} P≈51.87 mP \approx 51.87 \text{ m}

    Perimita ya umbo ni 51.87 m\boxed{\text{51.87 m}}.

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