Subjects geometry

Circle Area Scale

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1. The problem states that we have a circle and a scaled copy of the circle with a scale factor of 2. 2. We want to compare the area of the scaled copy to the area of the original circle. 3. The formula for the area of a circle is $$A = \pi r^2$$ where $r$ is the radius. 4. When a figure is scaled by a factor of $k$, the new radius becomes $r' = k r$. 5. The area of the scaled circle is then $$A' = \pi (r')^2 = \pi (k r)^2 = \pi k^2 r^2 = k^2 \pi r^2$$. 6. This means the area scales by the square of the scale factor. 7. Given the scale factor $k = 2$, the area of the scaled circle is $$A' = 2^2 \times A = 4A$$. 8. Therefore, the area of the scaled copy is 4 times the area of the original circle. Final answer: The area of the scaled circle is 4 times larger than the area of the original circle.