Anonymous
Anonymous asked in Science & MathematicsMathematics · 8 months ago

# On a circle, a 210degree angle forms an arc with a length of 150cm. To the nearest tenth of a cm, the radius of the circle is?

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s = rΘ : Θ measured in radians

r = 150/Θ = 150/(210π/180) ≈ 40.9cm

Ans: 40.9 cm

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• :-

210/360 x C = 150

C = 36/21 x 150

C = 12/7 x 150

C = 1800/7

C = 257•1 cm

2π r = 257•1

r = 257•1/(2π)

r = 41.0 cm

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• Let’s determine the fraction of a circle.

Fraction = 210 ÷ 360 = 7/12

150 centimeters is 7/12th of the circle. To determine the circumference of this circle, divide 150 cm by this fraction.

Circumference = 150 * 12/7 = 1,800/7

This is approximately 257 centimeters. To determine the radius of the circle, divide the circumferemce by 2 * π.

r = 1,800/7 ÷ (2 * π) = 900 ÷ 7π

This is approximately 40.9 centimeters. I hope this is helpful for you.

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• 210° = 210π/180 = 7π/6 radians

7πr/6 = 150

r = 40.9 cm

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