A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $90 π$ $90 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $90 π$ $90 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-19T08:06:53

$= 11.176$ $=11.176$

Explanation:

A chord that goes from $\frac{π}{4}$ $(pi)/4$ to $\frac{5 π}{8}$ $(5pi)/8$
so it travels the distance $\frac{5 π}{8} - \frac{π}{4} = \frac{3 π}{8}$ $(5pi)/8-(pi)/4=(3pi)/8$ ;
or
$\frac{3 π}{8} \div 2 π = \frac{3}{16}$ $(3pi)/8-:2pi=3/16$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 90 π$ $=pir^2=90pi$
or
$r^{2} = 90$ $r^2=90$
or
$r = \sqrt{90}$ $r=sqrt90$
or
$r = 9.48$ $r=9.48$
Circumference of the circle $= 2 π r = 2 (π) (9.48) = 59.6$ $=2pir=2(pi)(9.48)=59.6$
Therefore Length of the chord $= 59.6 \times \frac{3}{16} = 11.176$ $=59.6times3/16=11.176$

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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $90 π$ $90 pi$ , what is the length of the chord?

1 Answer

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A circle has a chord that goes from π4pi/4 to 5π8(5 pi) / 8 radians on the circle. If the area of the circle is 90π90 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $90 π$ $90 pi$ , what is the length of the chord?