A circle has a chord that goes from #( pi)/3 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #15 pi #, what is the length of the chord?

Answer 1

Aaliyah Anderson

The length of the chord is #=2sqrt15=7.75#

The angle subtended by the chord at the center of the circle is

#theta=4/3pi-1/3pi=3/3pi=pi#

The chord is the diameter of the circle

Let the radius of the circle be #=r#

The area of the circle is #A=pir^2#

Here, #A=15pi#

So,

#pir^2=15pi#

#r^2=15#

#r=sqrt15#

The length of the chord is

#l=2*sqrt15=7.75#

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Answer 2

Sophia Alfred

To find the length of the chord, we first need to determine the radius of the circle. Then, we can use the formula for the length of a chord in a circle in terms of the radius and the central angle subtended by the chord. The central angle in this case is $\frac{4\pi}{3} - \frac{\pi}{3} = \pi$ radians. Finally, we can substitute the radius and the central angle into the formula to find the length of the chord.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.