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A sector has an arc length of 4π and a radius of 3. What is the centra
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04 Mar 2021, 06:00
04 Mar 2021, 06:00
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A sector has an arc length of 4π and a radius of 3. What is the central angle of the sector?
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
Re: A sector has an arc length of 4π and a radius of 3. What is the centra
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04 Mar 2021, 07:12
04 Mar 2021, 07:12
You can easily calculate the using the formula of arc length = (center angle / 360) * 2 * π * r
but, there is a more easy approach. Let's calculate the circumference first = 2 * π * r = 6 * π and the arc length is 4 * π
So, 6 * π will create an angle of 360° with the center cause it's covering the whole circle.
As, 4 * π is 2/3 of 6 * π the certer angle will be = 360° * (2 / 3) = 240°
Answer choice - D
but, there is a more easy approach. Let's calculate the circumference first = 2 * π * r = 6 * π and the arc length is 4 * π
So, 6 * π will create an angle of 360° with the center cause it's covering the whole circle.
As, 4 * π is 2/3 of 6 * π the certer angle will be = 360° * (2 / 3) = 240°
Answer choice - D
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Re: A sector has an arc length of 4π and a radius of 3. What is the centra
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04 Mar 2021, 07:36
04 Mar 2021, 07:36
1
GeminiHeat wrote:
A sector has an arc length of 4π and a radius of 3. What is the central angle of the sector?
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
A. 60°
B. 90°
C. 180°
D. 240°
E. 270°
Arc length \(= \frac{θ}{360}(2πr) = 4π\)
i.e. \(\frac{θ}{360}(3) = 2\)
\(\frac{θ}{120} = 2\)
\(θ = 240\)
Hence, option D
