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Bài tập 85 trang 100 SGK Toán 9 Tập 2

Giải bài 85 tr 100 sách GK Toán 9 Tập 2

Hình viên phân là hình tròn giới hạn bởi một cung tròn và dây căng cung ấy. Hãy tính diện tích hình viên phân AmB, biết góc ở tâm góc AOB bằng 60 độ và bán kính đường tròn là 5,1 cm (h.64)

Hình 64 bài 85 trang 99 SGK Toán 9 Tập 2

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Hướng dẫn giải chi tiết bài 85

 
 

Với bài 85 này, chúng ta sẽ được biết thêm khái niệm về hình viên phân, rất dễ dàng thấy rằng diện tích ấy bằng diện tích quạt trừ diện tích tam giác OAB.

Gọi H là chân đường vuông góc từ O đến AB.

Vậy H là trung điểm AB

OAB là tam giác đều có cạnh bằng \(\small R = 5,1cm\)

\(\small \Rightarrow AH=\frac{5,1}{2}=2,55(cm)\)

\(\small \Rightarrow OH=\sqrt{OA^2-AH^2}=2,55\sqrt{3}(cm)\)

Vậy diện tích của tam giác AOB đều là:

\(\small S_{AOB}=\frac{1}{2}OH.AB=2,55.5,1\sqrt{3}.\frac{1}{2}=\approx 11,26(cm^2)\)

Diện tích quạt tròn AOB là:

\(\small S_q=\frac{\pi 5,1^2}{6}\approx 13,62(cm^2)\)

Diện tích viên phân cần tính là:

\(\small S=S_q-S_{ABC}\approx2,35(cm^2)\)

-- Mod Toán 9 HỌC247

 
Nếu bạn thấy hướng dẫn giải Bài tập 85 trang 100 SGK Toán 9 Tập 2 HAY thì click chia sẻ 
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  • bach dang

    a) Vẽ lại hình tạo bởi các cung tròn xuất phát từ đỉnh C của tam giác đều ABC cạnh 1 cm. Nêu cách vẽ.

    b) Tính diện tích miền gạch sọc.

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<clippath id=\"clip3\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_9\"><path> <clippath> <g clip-path=\"url(#clip3)\" id=\"svg_10\"> <g fill=\"none\" id=\"svg_11\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m198.78,196.89c0.16,20.01 10.98,38.41 28.38,48.27c17.41,9.87 38.76,9.7 56,-0.44\" id=\"svg_12\"><path> <title><title> <desc>Cung c: CungTròn[A, C, D]<desc> <g> <!-- drawing style --> <g> <!-- clip3 --> <clippath id=\"clip4\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_13\"><path> <clippath> <g clip-path=\"url(#clip4)\" id=\"svg_14\"> <g fill=\"none\" id=\"svg_15\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m283.16,244.72c34.5,-20.28 55.55,-57.43 55.23,-97.44c-0.31,-40.01 -21.96,-76.818 -56.77,-96.55\" id=\"svg_16\"><path> <title><title> <desc>Cung d: CungTròn[B, D, E]<desc> <g> <!-- drawing style --> <g> <!-- clip4 --> <clippath id=\"clip5\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_17\"><path> <clippath> <g clip-path=\"url(#clip5)\" id=\"svg_18\"> <g fill=\"none\" id=\"svg_19\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m281.62,50.73c-52.21,-29.598 -116.26,-29.09 -168,1.333c-51.738,30.423 -83.319,86.137 -82.842,146.157\" id=\"svg_20\"><path> <title><title> <desc>Cung e: CungTròn[C, E, F]<desc> <g> <!-- drawing style --> <g> <!-- clip5 --> <clippath id=\"clip6\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_21\"><path> <clippath> <g clip-path=\"url(#clip6)\" id=\"svg_22\"> <g fill=\"none\" id=\"svg_23\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m198.78,196.89l56,-0.45\" id=\"svg_24\"><path> <title><title> <desc>Đoạn thẳng f: Đoạn thẳng [C, A] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip6 --> <clippath id=\"clip7\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_25\"><path> <clippath> <g clip-path=\"url(#clip7)\" id=\"svg_26\"> <g fill=\"none\" id=\"svg_27\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m254.78,196.44l-28.39,-48.27\" id=\"svg_28\"><path> <title><title> <desc>Đoạn thẳng g: Đoạn thẳng [A, B] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip7 --> <clippath id=\"clip8\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_29\"><path> <clippath> <g clip-path=\"url(#clip8)\" id=\"svg_30\"> <g fill=\"none\" id=\"svg_31\" stroke=\"#993300\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m226.39,148.17l-27.61,48.72\" id=\"svg_32\"><path> <title><title> <desc>Đoạn thẳng h: Đoạn thẳng [B, C] của Hình đa giác TenDaGiac1<desc> <g> <!-- drawing style --> <g> <!-- clip8 --> <clippath id=\"clip9\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_33\"><path> <clippath> <g clip-path=\"url(#clip9)\" id=\"svg_34\"> <g fill=\"none\" id=\"svg_35\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m254.78,196.44l28.38,48.28\" id=\"svg_36\"><path> <title><title> <desc>Đoạn thẳng i: Đoạn thẳng [A, D]<desc> <g> <!-- drawing style --> <g> <!-- clip9 --> <clippath id=\"clip10\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_37\"><path> <clippath> <g clip-path=\"url(#clip10)\" id=\"svg_38\"> <g fill=\"none\" id=\"svg_39\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m226.39,148.17l55.23,-97.44\" id=\"svg_40\"><path> <title><title> <desc>Đoạn thẳng j: Đoạn thẳng [B, E]<desc> <g> <!-- drawing style --> <g> <!-- clip10 --> <clippath id=\"clip11\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_41\"><path> <clippath> <g clip-path=\"url(#clip11)\" id=\"svg_42\"> <g fill=\"none\" id=\"svg_43\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m30.778,198.22l168.002,-1.33\" id=\"svg_44\"><path> <title><title> <desc>Đoạn thẳng k: Đoạn thẳng [F, C]<desc> <g> <!-- drawing style --> <g> <!-- clip11 --> <clippath id=\"clip12\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_45\"><path> <clippath> <g clip-path=\"url(#clip12)\" id=\"svg_46\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_47\"> <path d=\"m203.78,196.89c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_48\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip12 --> <clippath id=\"clip13\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_49\"><path> <clippath> <g clip-path=\"url(#clip13)\" id=\"svg_50\"> <g fill=\"none\" id=\"svg_51\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m203.78,196.89c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_52\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip13 --> <clippath id=\"clip14\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_53\"><path> <clippath> <g clip-path=\"url(#clip14)\" id=\"svg_54\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_55\"> <path d=\"m183.11,216.97l2.28,0.58q-0.72,2.79 -2.58,4.27q-1.86,1.48 -4.54,1.48q-2.77,0 -4.51,-1.14q-1.74,-1.13 -2.65,-3.28q-0.91,-2.15 -0.91,-4.6q0,-2.69 1.03,-4.69q1.02,-2 2.91,-3.03q1.89,-1.03 4.17,-1.03q2.58,0 4.34,1.31q1.76,1.32 2.44,3.69l-2.23,0.53q-0.61,-1.87 -1.74,-2.73q-1.14,-0.86 -2.85,-0.86q-1.99,0 -3.32,0.95q-1.33,0.96 -1.86,2.55q-0.54,1.59 -0.54,3.3q0,2.18 0.63,3.82q0.63,1.64 1.98,2.45q1.36,0.8 2.92,0.8q1.92,0 3.24,-1.1q1.32,-1.1 1.79,-3.27z\" id=\"svg_56\"><path> <title><title> <desc>C = (30.6, -24.92)<desc> <g> <!-- drawing style --> <g> <!-- clip14 --> <clippath id=\"clip15\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_57\"><path> <clippath> <g clip-path=\"url(#clip15)\" id=\"svg_58\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_59\"> <path d=\"m259.78,196.44c0,2.77 -2.24,5 -5,5c-2.76,0 -5,-2.23 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_60\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip15 --> <clippath id=\"clip16\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_61\"><path> <clippath> <g clip-path=\"url(#clip16)\" id=\"svg_62\"> <g fill=\"none\" id=\"svg_63\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m259.78,196.44c0,2.77 -2.24,5 -5,5c-2.76,0 -5,-2.23 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_64\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip16 --> <clippath id=\"clip17\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_65\"><path> <clippath> <g clip-path=\"url(#clip17)\" id=\"svg_66\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_67\"> <path d=\"m258.97,186l6.59,-17.19l2.46,0l7.03,17.19l-2.6,0l-2,-5.2l-7.18,0l-1.89,5.2l-2.41,0zm4.95,-7.06l5.83,0l-1.8,-4.75q-0.81,-2.17 -1.22,-3.57q-0.32,1.66 -0.92,3.29l-1.89,5.03z\" id=\"svg_68\"><path> <title><title> <desc>A = (49.73, -24.77)<desc> <g> <!-- drawing style --> <g> <!-- clip17 --> <clippath id=\"clip18\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_69\"><path> <clippath> <g clip-path=\"url(#clip18)\" id=\"svg_70\"> <g fill=\"#444444\" fill-rule=\"nonzero\" id=\"svg_71\"> <path d=\"m231.39,148.17c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_72\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip18 --> <clippath id=\"clip19\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_73\"><path> <clippath> <g clip-path=\"url(#clip19)\" id=\"svg_74\"> <g fill=\"none\" id=\"svg_75\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m231.39,148.17c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_76\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip19 --> <clippath id=\"clip20\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_77\"><path> <clippath> <g clip-path=\"url(#clip20)\" id=\"svg_78\"> <g fill=\"#444444\" fill-rule=\"nonzero\" id=\"svg_79\"> <path d=\"m213.77,137l0,-17.19l6.43,0q1.97,0 3.16,0.53q1.19,0.52 1.87,1.61q0.68,1.08 0.68,2.27q0,1.09 -0.61,2.07q-0.6,0.98 -1.8,1.57q1.56,0.45 2.4,1.55q0.83,1.11 0.83,2.61q0,1.2 -0.5,2.24q-0.51,1.04 -1.26,1.6q-0.75,0.56 -1.88,0.85q-1.14,0.29 -2.78,0.29l-6.54,0zm2.26,-9.97l3.72,0q1.52,0 2.17,-0.19q0.86,-0.26 1.3,-0.86q0.44,-0.59 0.44,-1.5q0,-0.86 -0.41,-1.5q-0.41,-0.65 -1.17,-0.89q-0.77,-0.25 -2.61,-0.25l-3.44,0l0,5.19zm0,7.94l4.28,0q1.1,0 1.55,-0.08q0.78,-0.14 1.31,-0.47q0.53,-0.33 0.87,-0.95q0.34,-0.63 0.34,-1.45q0,-0.96 -0.5,-1.67q-0.49,-0.71 -1.36,-1q-0.88,-0.29 -2.52,-0.29l-3.97,0l0,5.91z\" id=\"svg_80\"><path> <title><title> <desc>Điểm B: DaGiac[C, A, 3]<desc> <g> <!-- drawing style --> <g> <!-- clip20 --> <clippath id=\"clip21\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_81\"><path> <clippath> <g clip-path=\"url(#clip21)\" id=\"svg_82\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_83\"> <path d=\"m288.16,244.72c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_84\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip21 --> <clippath id=\"clip22\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_85\"><path> <clippath> <g clip-path=\"url(#clip22)\" id=\"svg_86\"> <g fill=\"none\" id=\"svg_87\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m288.16,244.72c0,2.76 -2.24,5 -5,5c-2.76,0 -5,-2.24 -5,-5c0,-2.76 2.24,-5 5,-5c2.76,0 5,2.24 5,5z\" id=\"svg_88\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip22 --> <clippath id=\"clip23\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_89\"><path> <clippath> <g clip-path=\"url(#clip23)\" id=\"svg_90\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_91\"> <path d=\"m291.86,275l0,-17.19l5.91,0q2.01,0 3.06,0.25q1.48,0.35 2.51,1.24q1.36,1.14 2.04,2.93q0.68,1.79 0.68,4.08q0,1.96 -0.46,3.47q-0.46,1.52 -1.17,2.51q-0.71,0.99 -1.56,1.55q-0.85,0.57 -2.06,0.86q-1.2,0.3 -2.76,0.3l-6.19,0zm2.26,-2.03l3.68,0q1.7,0 2.66,-0.31q0.96,-0.32 1.54,-0.89q0.81,-0.82 1.27,-2.18q0.45,-1.37 0.45,-3.31q0,-2.7 -0.89,-4.15q-0.89,-1.44 -2.16,-1.93q-0.9,-0.36 -2.94,-0.36l-3.61,0l0,13.13z\" id=\"svg_92\"><path> <title><title> <desc>Điểm D: C xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip23 --> <clippath id=\"clip24\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_93\"><path> <clippath> <g clip-path=\"url(#clip24)\" id=\"svg_94\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_95\"> <path d=\"m286.62,50.73c0,2.761 -2.24,5 -5,5c-2.76,0 -5,-2.239 -5,-5c0,-2.761 2.24,-5 5,-5c2.76,0 5,2.239 5,5z\" id=\"svg_96\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip24 --> <clippath id=\"clip25\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_97\"><path> <clippath> <g clip-path=\"url(#clip25)\" id=\"svg_98\"> <g fill=\"none\" id=\"svg_99\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m286.62,50.73c0,2.761 -2.24,5 -5,5c-2.76,0 -5,-2.239 -5,-5c0,-2.761 2.24,-5 5,-5c2.76,0 5,2.239 5,5z\" id=\"svg_100\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip25 --> <clippath id=\"clip26\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_101\"><path> <clippath> <g clip-path=\"url(#clip26)\" id=\"svg_102\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_103\"> <path d=\"m287.91,41l0,-17.188l12.42,0l0,2.032l-10.16,0l0,5.265l9.5,0l0,2.016l-9.5,0l0,5.844l10.55,0l0,2.031l-12.81,0z\" id=\"svg_104\"><path> <title><title> <desc>Điểm E: D xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip26 --> <clippath id=\"clip27\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_105\"><path> <clippath> <g clip-path=\"url(#clip27)\" id=\"svg_106\"> <g fill=\"#0000ff\" fill-rule=\"nonzero\" id=\"svg_107\"> <path d=\"m35.778,198.22c0,2.76 -2.239,5 -5,5c-2.762,0 -5,-2.24 -5,-5c0,-2.76 2.238,-5 5,-5c2.761,0 5,2.24 5,5z\" id=\"svg_108\"><path> <title><title> <desc>Điểm F: E xoay bởi góc 120°<desc> <g> <!-- drawing style --> <g> <!-- clip27 --> <clippath id=\"clip28\"> <path d=\"m0,0l0,753l1048,0l0,-753l-1048,0z\" id=\"svg_109\"><path> <clippath> <g clip-path=\"url(#clip28)\" id=\"svg_110\"> <g fill=\"none\" id=\"svg_111\" stroke=\"#000000\" stroke-linecap=\"round\" stroke-linejoin=\"round\"> <path d=\"m35.778,198.22c0,2.76 -2.239,5 -5,5c-2.762,0 -5,-2.24 -5,-5c0,-2.76 2.238,-5 5,-5c2.761,0 5,2.24 5,5z\" id=\"svg_112\"><path> <title><title> <desc>Điểm F: E xoay bởi góc 120°<desc> <g> <!-- 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