$\"\"$ \ \

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The area of the region covered by sand is equal to the area of the large is $\"\"$ .

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The rectangular equation of large circle is $\"\"$ .

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Change the equation $\"\"$ in to standard form using completing square method.

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$\"\"$

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$\"\"$

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$\"\"$ .

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The equation is in the form of standard form of circle equation $\"\"$ , where $\"\"$ is the center of the circle and $\"\"$ is the radius of the circle.

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Here, center is $\"\"$ and radius is $\"\"$ .

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The area of the circle is $\"\"$ .

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The area of the large circle is $\"\"$ .

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$\"\"$

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The polar equation of the small circle is $\"\"$ .

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Convert polar equation to rectangular equation.

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$\"\"$

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$\"\"$

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$\"\"$

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Substitute $\"\"$ , $\"\"$ and $\"\"$ .

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ .

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Center is $\"\"$ and radius is $\"\"$ .

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The area of the large circle is $\"\"$ .

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The area of the region covered by sand is equal to the area of the large is $\"\"$ .

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$\"\"$

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$\"\"$ .

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The area of the region covered by sand is equal to the area of the large is $\"\"$ .

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$\"\"$

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The area of the region covered by sand is equal to the area of the large is $\"\"$ . \ \