A chord with a length of $4$ $4$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

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A chord with a length of $4$ $4$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

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Answer 1 · 2016-03-02T05:45:37

$733.386$ $733.386$

Explanation:

As the chord with a length of $4$ $4$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{3}$ $pi/3$ radians, it is obvious that it subtends an angle of $\frac{π}{3} - \frac{π}{4} = \frac{π}{12}$ $pi/3-pi/4=pi/12$ .

Hence complete circumference, which subtends an angle of $2 π$ $2pi$ should be of length

$4 \times \frac{2 π}{\frac{π}{12}} = 4 \times 2 π \times \frac{12}{π}$ $4xx(2pi)/(pi/12)=4xx2pixx12/pi$ i.e. $96$ $96$ .

Hence, radius of circle is $\frac{96}{2 π} = \frac{48}{π}$ $96/(2pi)=48/pi$ , and area of circle will be

$π \times {(\frac{48}{π})}^{2} = 48 \times \frac{48}{π} = 733.386$ $pixx(48/pi)^2=48xx48/pi=733.386$

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A chord with a length of $4$ $4$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

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Explanation:

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