Question #7a536

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Question #7a536

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Answer 1 · 2017-05-29T16:50:44

if the circumference is $9 π$ $9pi$ , then $A \approx 3.53$ $A ~~3.53$ , but if the area of the whole circle is $9 π$ $9pi$ , then $A = \frac{π}{2}$ $A =pi/2$

Explanation:

So I'm asuming you have a circle with a circumference of $9 π$ $9pi$ in wich you want the area of a sector?

If the angle that forms the sector is given in radians, then we can use the formula: $A = \frac{1}{2} r^{2} θ$ $A=1/2r^2theta$
In this case, $θ = \frac{1}{9} π$ $theta=1/9pi$

We don't know the radius, therefore we must find it first.
The circumference of a circle is given by: $O = 2 r π$ $O = 2rpi$
Therefore:
$9 π = 2 r π \Leftrightarrow 9 = 2 r \Leftrightarrow r = 4.5$ $9pi=2rpi iff 9=2r iff r = 4.5$

Now we can calculate the area of the sector: $A = \frac{1}{2} \cdot {4.5}^{2} \cdot \frac{1}{9} π \approx 3.53$ $A=1/2*4.5^2*1/9pi ~~ 3.53$

... Or maybe, you meant the are of the whole circle is $9 π$ $9pi$ in many ways this would make more sense.

The solution is found in a similar way, only we will have to define two areas. The area for the whole circle and the area of the sector:
Aw is the area of the Whole circle.
$A_{w} = r^{2} π = 9 π$ $A_"w" = r^2pi = 9pi$

Isolate "r".

$r^{2} π = 9 π \Leftrightarrow r^{2} = 9 \Leftrightarrow r = \sqrt{9} = 3$ $r^2pi = 9pi iff r^2=9 iff r = sqrt9=3$

Now calculate the area of the sector in the same way we did before:

$A_{s} = \frac{1}{2} \cdot 3^{2} \cdot \frac{1}{9} π = \frac{π}{2}$ $A_"s"=1/2*3^2*1/9pi = pi/2$

This answer looks much better, which is why I think this is more correct.

Sorry for the inconvienience

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