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What is area of the sector ACBO
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15 Jun 2021, 07:58
15 Jun 2021, 07:58
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Question Stats:
91% (01:34) correct
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What is area of the sector ACBO in the circle above with center O, if the radius of the circle is 6 and the length of the arc ACB is 2π?
A. \(6\pi\)
B. \(6\pi - 6\)
C. \(6\pi - 9\)
D. \(6\pi-\frac{25}{2}\)
E. \(6\pi-9\sqrt{3}\)
What is area of the sector ACBO
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15 Jun 2021, 08:18
15 Jun 2021, 08:18
1
Solution:
As we are given radius, we can find the circumference of the whole circle= 2πr=12π
But, we are also given, that the length of the arc ACBO= 2π. Which is\(\frac{ 1}{6}\)th of the whole circle.
Therefore, arc ACBO is \(\frac{ 1}{6}\)th of the whole circle
Area of the whole circle=\(πr^2\)=36π
Area of the region ACBO=\( \frac{36π}{6}\)=6π
IMO A
Hope this helps!
As we are given radius, we can find the circumference of the whole circle= 2πr=12π
But, we are also given, that the length of the arc ACBO= 2π. Which is\(\frac{ 1}{6}\)th of the whole circle.
Therefore, arc ACBO is \(\frac{ 1}{6}\)th of the whole circle
Area of the whole circle=\(πr^2\)=36π
Area of the region ACBO=\( \frac{36π}{6}\)=6π
IMO A
Hope this helps!
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Re: What is area of the sector ACBO
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15 Jun 2021, 09:40
15 Jun 2021, 09:40
1
Carcass wrote:
What is area of the sector ACBO in the circle above with center O, if the radius of the circle is 6 and the length of the arc ACB is 2π?
A. \(6\pi\)
B. \(6\pi - 6\)
C. \(6\pi - 9\)
D. \(6\pi-\frac{25}{2}\)
E. \(6\pi-9\sqrt{3}\)
Circumference = 2π(radius)
Given: radius is 6
So, circumference = 2π(6) = 12π
We're told the arc ACB has length 2π
2π/12π = 1/6.
So, the arc represents 1/6 of the circle's entire circumference
This also means sector ACBO represents 1/6 of the circle's area
Area of circle = π(radius)²
So, area of this circle = π(6)² = 36π
So, the area of sector ACBO = 1/6 of 36π
= 6π
Answer: A
Cheers,
Brent
