# 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?

Relevance

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

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• 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

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