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The square in the figure has two sides tangent to the circle. If area of the circle is 9a^2pi^2, find the area of the square. (A=6, pi=3.14, please estimate the answer two places after decimal)

The Square In The Figure Has Two Sides Tangent To The Circle If Area Of The Circle Is 9a2pi2 Find The Area Of The Square A6 Pi314 Please Estimate The Answer Two class=

Sagot :

As the square has two sides tangent to the circle, the lenght of the side will be de diameter of the circle.

The area of a circle, which is pi*r², in this case is 9a²pi², given that a=6.

So:

[tex]\begin{gathered} \pi r^2=9\cdot a^2\cdot\pi^2\text{ (dividing both sides by pi)} \\ \pi r^2=9\cdot36\cdot3.14^{2} \\ \pi r^{2}=3,194,51 \\ r^{2}=1017,36 \\ r=31,89 \end{gathered}[/tex]

Once r=31.89,, the diameter will be 2*r= 63.78

The area of the square is (63.78)² = 4,067.89u²

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