A circle has a chord that goes from 2π3 to 5π8 radians on the circle. If the area of the circle is 120π, what is the length of the chord?

Step 1 A chord that goes from 2π3 to 5π8 so it travels the distance 2π3−5π8=π24 or π24÷2π=148 of the Circumference of the Circle Area of the Circle =πr2=120π or r2=120 or r=120 or r=10.95 Circumference of the circle =2πr=2(π)(10.95)=68.83 Therefore Length of the chord =68.83(148)=1.43

Answered: "A circle has a chord that goes from..."

High School
Geometry
High school geometry
Circles

Kai Lin

Answered question

2022-02-09

A circle has a chord that goes from

\frac{2 π}{3}

\frac{5 π}{8}

radians on the circle. If the area of the circle is

120 π

, what is the length of the chord?

Answer & Explanation

Vaughn Bradley

Beginner2022-02-10Added 16 answers

Step 1
A chord that goes from

2 \frac{π}{3}

5 \frac{π}{8}

so it travels the distance

2 \frac{π}{3} - 5 \frac{π}{8} = \frac{π}{24}

\frac{π}{24} \div 2 π = \frac{1}{48}

of the Circumference of the Circle
Area of the Circle

= π r^{2} = 120 π

r^{2} = 120

r = \sqrt{120}

r = 10.95

Circumference of the circle

= 2 π r = 2 (π) (10.95) = 68.83

Therefore Length of the chord

= 68.83 (\frac{1}{48}) = 1.43

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