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A sector of a circle has a radius of 10 and an area of 20π.
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19 Sep 2018, 17:50
19 Sep 2018, 17:50
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A sector of a circle has a radius of 10 and an area of 20π. What is the arc length of the sector?
(A) \(\pi\)
(B) \(2\pi\)
(C) \(4\pi\)
(D) \(5\pi\)
(E) \(10\pi\)
(A) \(\pi\)
(B) \(2\pi\)
(C) \(4\pi\)
(D) \(5\pi\)
(E) \(10\pi\)
Re: A sector of a circle has a radius of 10 and an area of 20π.
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15 Apr 2020, 06:23
15 Apr 2020, 06:23
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sandy wrote:
A sector of a circle has a radius of 10 and an area of 20π. What is the arc length of the sector?
(A) \(\pi\)
(B) \(2\pi\)
(C) \(4\pi\)
(D) \(5\pi\)
(E) \(10\pi\)
(A) \(\pi\)
(B) \(2\pi\)
(C) \(4\pi\)
(D) \(5\pi\)
(E) \(10\pi\)
We know,
\(\frac{{Area of the sector}}{ {Area of the circle}} = \frac{{Arc length}}{{circumference}}\)
Area of the circle = \(20\pi\)
Area of the sector = \(100\pi\)
Circumference of the circle = \(2 * 10 * radius = 20\pi\)
Therefore,
\(\frac{{20\pi}}{{100\pi}} = \frac{Arc}{{20\pi}}\)
or Arc length = \(4\pi\)
Re: A sector of a circle has a radius of 10 and an area of 20π.
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12 May 2020, 21:50
12 May 2020, 21:50
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A sector of a circle has a radius of 10 and an area of 20π. What is the arc length of the sector?
The radius of the circle = radius of the sector
Area of the circle is \(100\pi\)
Area of the sector = \(20\pi\)
The sector area is one-fifth of the area of the circle \((\frac{{100\pi}}{{20\pi}} = 5)\)
Therefore, by the well known ratios relating the areas, circumference and central angle of the full circle and a sector of the circle,
\(\frac{{Area of Sector}}{{Area of Circle}} = \frac{Arc Length of Sector}{Circumference of the Circle} = \frac{Central Angle of Sector}{Full Angle of Circle}\)
We can deduce that the Arc Length of the Sector will be one-fifth of the Circumference of the Circle.
Circumference of the Circle = \(2\pi*10 = 20\pi\)
Therefore, Arc Length of the Sector = \(\frac{{20\pi}}{{5}} = 4\pi\)
The Answer is C.
The radius of the circle = radius of the sector
Area of the circle is \(100\pi\)
Area of the sector = \(20\pi\)
The sector area is one-fifth of the area of the circle \((\frac{{100\pi}}{{20\pi}} = 5)\)
Therefore, by the well known ratios relating the areas, circumference and central angle of the full circle and a sector of the circle,
\(\frac{{Area of Sector}}{{Area of Circle}} = \frac{Arc Length of Sector}{Circumference of the Circle} = \frac{Central Angle of Sector}{Full Angle of Circle}\)
We can deduce that the Arc Length of the Sector will be one-fifth of the Circumference of the Circle.
Circumference of the Circle = \(2\pi*10 = 20\pi\)
Therefore, Arc Length of the Sector = \(\frac{{20\pi}}{{5}} = 4\pi\)
The Answer is C.
