Smile 發問時間: 科學及數學數學 · 2 個月前

Maths problem, how to do, thanks?

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2 個解答

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  • SC147
    Lv 6
    2 個月前
    最佳解答

    (a) Let mid-pt. of AB = M

    sin 60⁰ = AM/9

    AM = 9 sin 60⁰ = 9√3/2

    ∴ AB = 2(9√3/2) = 9√3 = 15.6 cm  (to 3 sig.fig.)

    (b) Arc AB = 2π(9)(120/360) ---------→ 《arc length = 2πr(θ/360)》

         = 6π 

    ∴ perimeter of shaded region =  6π + 9√3 = 34.4 cm (to 3 sig.fig.)

    (c) area of sector = π(9²)(120/360) -→ 《area of sector = πr²(θ/360)》

             = 27π

    area of △OAB = ½(9)(9)sin120⁰  --→《area of △ = ½ absinθ, where θ- included ∠》

            = (81/2)(√3/2)

            = 81√3/4

    ∴ area of shaded region = 27π -  81√3/4 = 49.7 cm² (to 3 sig.fig.) 

  • 1 個月前

    SC老師謝謝您,這題我看明白了,之前我想不通,原來AB線只要按你说加中點,就可以解決了,谢谢你.

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