A chord with a length of $15$ $15$ runs from $\frac{π}{8}$ $pi/8$ 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 $15$ $15$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

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Answer 1 · 2018-01-18T12:54:57

Area of the circle $A_{c} = π r^{2} = π {(23.3325)}^{2} = 1710.3$ $A_c = pi r^2 = pi (23.3325)^2 = color (purple)(1710.3)$ sq. units

Explanation:

Length of the chord $L_{c} = 15$ $L_c = 15$ given

Center angle subtended by the chord $θ = (\frac{π}{3}) - (\frac{π}{8}) = \frac{5 π}{24}$ $theta = (pi/3) - (pi/8) = (5pi)/24$

$\frac{θ}{2} = (\frac{5 π}{48})$ $theta / 2 = ((5pi)/48)$

Radius of the circle $r = \frac{L_{c}}{2 \cdot sin (\frac{θ}{2})} = \frac{15}{2 \cdot sin (\frac{5 π}{48})} = 23.3325$ $r = L_c / (2*sin (theta/2) )= 15 / (2 * sin ((5pi)/48) )= color (red)(23.3325)$

Area of the circle $A_{c} = π r^{2} = π {(23.3325)}^{2} = 1710.3$ $A_c = pi r^2 = pi (23.3325)^2 = color (purple)(1710.3)$ sq. units

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A chord with a length of $15$ $15$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?

1 Answer

Explanation:

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A chord with a length of $15$ $15$ runs from $\frac{π}{8}$ $pi/8$ to $\frac{π}{3}$ $pi/3$ radians on a circle. What is the area of the circle?