A circle has a chord that goes from $\frac{π}{8}$ $( pi)/8$ to $\frac{5 π}{6}$ $(5 pi) / 6$ radians on the circle. If the area of the circle is $225 π$ $225 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{8}$ $( pi)/8$ to $\frac{5 π}{6}$ $(5 pi) / 6$ radians on the circle. If the area of the circle is $225 π$ $225 pi$ , what is the length of the chord?

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Answer 1 · 2016-08-10T20:56:36

$= 33.38$ $=33.38$

Explanation:

A chord that goes from $\frac{π}{8}$ $(pi)/8$ to $\frac{5 π}{6}$ $(5pi)/6$
so it travels the distance $\frac{5 π}{6} - \frac{π}{8} = \frac{17 π}{24}$ $(5pi)/6-(pi)/8=(17pi)/24$ ;
or
$\frac{17 π}{24} \div 2 π = \frac{17}{48}$ $(17pi)/24-:2pi=17/48$ of the Circumference of the Circle
Area of the Circle $= π r^{2} = 225 π$ $=pir^2=225pi$
or
$r^{2} = 225$ $r^2=225$
or
$r = \sqrt{225}$ $r=sqrt225$
or
$r = 15$ $r=15$
Circumference of the circle $= 2 π r = 2 (π) (15) = 94.24$ $=2pir=2(pi)(15)=94.24$
Therefore Length of the chord $= 94.24 \times \frac{17}{48} = 33.38$ $=94.24times17/48=33.38$

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A circle has a chord that goes from $\frac{π}{8}$ $( pi)/8$ to $\frac{5 π}{6}$ $(5 pi) / 6$ radians on the circle. If the area of the circle is $225 π$ $225 pi$ , what is the length of the chord?

1 Answer

Explanation:

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A circle has a chord that goes from π8( pi)/8 to 5π6(5 pi) / 6 radians on the circle. If the area of the circle is 225π225 pi , what is the length of the chord?

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Explanation:

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A circle has a chord that goes from $\frac{π}{8}$ $( pi)/8$ to $\frac{5 π}{6}$ $(5 pi) / 6$ radians on the circle. If the area of the circle is $225 π$ $225 pi$ , what is the length of the chord?