A chord with a length of $1$ $1$ runs from $\frac{π}{4}$ $pi/4$ 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 $1$ $1$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

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Answer 1 · 2017-10-13T02:18:13

Area $=$ $=$ 5.363 $a$ $color(white)(a)$ sq.units

Explanation:

Angle at the center $= \frac{π}{2} - \frac{π}{4} = \frac{π}{4}$ $=pi/2-pi/4=pi/4$
Base angle each $= \frac{π - (\frac{π}{4})}{2} = \frac{3 π}{8}$ $=(pi-(pi/4))/2=(3pi)/8$
$r \cdot cos (\frac{3 π}{8}) = \frac{1}{2}$ $r*cos((3pi)/8)=1/2$
$r = \frac{\frac{1}{2}}{cos (\frac{3 π}{8})} = 1.3066$ $r=(1/2)/cos((3pi)/8)=1.3066$

Area of the circle $= π \cdot r^{2} = (\frac{22}{7}) \cdot {1.3066}^{2} = 5.363$ $=pi*r^2=(22/7)*1.3066^2=5.363$

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A chord with a length of $1$ $1$ runs from $\frac{π}{4}$ $pi/4$ to $\frac{π}{2}$ $pi/2$ radians on a circle. What is the area of the circle?

1 Answer

Explanation:

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