I need help with some sector of a circle probelms?

A sector of a circle has area 90cm^2 and central 0.2 radians. Find its radius and arc length..

A sector of a circle has central angle 24 degrees and arc length 8.4cm. Find its area to the nearest square centimeter.

At its closest approach, Mars is about 5.6*10^7 km from earth and its apparent size is about 0.00012 radians. What is the approximate diameter of Mars?

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  • Shy
    Lv 6
    10 years ago
    Favorite Answer

    Hi John

    1.

    A sector of a circle has area 90cm^2 and central 0.2 radians. Find its radius and arc length..

    Area of sector = θ/360*π*r^2 where r is the radius and θ the central angle

    θ/360*π*r^2 = 90

    0.2*180/360*π*r^2 = 90

    r^2 = 900/π

    r = 9.56 cms

    Arc length = θ/360 * 2π*r = 0.2*180/360*2π*9.56

    Arc length = 6 cms

    2.

    A sector of a circle has central angle 24 degrees and arc length 8.4cm. Find its area to the nearest square centimeter.

    Arc length = θ/360 * 2π*r

    24/360 * 2π*r = 8.4

    r = 20 cms

    So

    Area of sector = θ/360*π*r^2

    Area of sector = 24/360*π*20^2

    Area of sector = 24/360*π*20^2 = (80/3)π

    Area of sector = 84 cm^2

    3.

    At its closest approach, Mars is about 5.6*10^7 km from earth and its apparent size is about 0.00012 radians. What is the approximate diameter of Mars?

    Dia of Mars = θ/360 * 2π*r

    Dia = .00012*180/360 * 2π* 5.6*10^7

    Dia = 2/10^5*2π* 5.6*10^7 = 22.4*π*10^2 kms = 7037 kms

    Dia = 7037000 meters or approx 7*10^6 meters

    Shy

  • 10 years ago

    1.

    A = 90 * (2*pi) / 0.2

    A = 900*pi

    A = pi*r^2

    pi*r^2 = 900*pi

    r^2 = 900

    r = sqrt(900)

    r = 30

    Arc length is 0.2 * 30 = 6 cm

    2.

    Circumference is 8.4 * (360/24) = 126 cm

    C = pi*d

    d = 2r

    C = 2*pi*r

    r = C / (2*pi)

    r = 126 / (2*pi)

    r = 63/pi

    A = pi*r^2

    A = pi*(63/pi)^2

    A = pi * (3969/pi^2)

    A = 3969/pi

    A =~ 1263 cm^2

    3.

    Use the Law of Cosines:

    c^2 = a^2 + b^2 - 2ab cos C

    a = b = 5.6 * 10^7 = 56,000,000

    C = 0.00012 radians

    c^2 = 56,000,000^2 + 56,000,000^2 - 2*56,000,000*56,000,000*cos(0.00012 radians)

    c^2 = 3136000000000000 + 3136000000000000 - 6272000000000000*cos(0.00012 radians)

    c = sqrt(6272000000000000 - 6272000000000000*cos(0.00012 radians))

    c =~ 6720 km

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