A chord with a length of $8$ $8$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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A chord with a length of $8$ $8$ runs from $\frac{π}{12}$ $pi/12$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2016-08-11T19:54:55

$= 117.34$ $=117.34$

Explanation:

The chord covers $\frac{π}{2} - \frac{π}{12} = \frac{5 π}{12}$ $pi/2-pi/12=(5pi)/12$ radians
Therefore we can write
The chord covers $\frac{5 π}{12} \div 2 π = \frac{5}{24}$ $(5pi)/12-:2pi=5/24$ of Circumference of the Circle $i . e$ $i.e$ ( $2 π r$ $2pir$ ;where $r$ $r$ is the radius of the Circle)
or
$\frac{5}{24} (2 π r) = 8$ $5/24(2pir)=8$
or
$2 π r = 8 \times \frac{24}{5}$ $2pir=8times24/5$
or
$r = 8 \times \frac{24}{5} \times \frac{1}{2 π}$ $r=8times24/5times1/(2pi)$
or
$r = 6.11$ $r=6.11$
Area of the Circle $= π r^{2}$ $=pir^2$
$= π {(6.11)}^{2}$ $=pi(6.11)^2$
$= 117.34$ $=117.34$

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1 Answer

Explanation:

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