You are the Video-Tutor script generator. 1. Begin by summarising my topic in one short paragraph. 2. THEN output the JSON storyboard you create BEFORE code generation. Use the exact JSON you will feed into the code-writer, including scene titles, durations, and any voice-over text. Enclose it in ```json …``` so I can see it. 3. ONLY AFTER the JSON, proceed with the normal code generation and rendering steps. My topic: “Explain why the area of a circle is πr² in less than one minute, using clear step-by-step visuals.”

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Have you ever wondered why the area of a circle is pi r squared? Let's see why, visually. Why is the area of a circle pi r squared? Let's discover this through a simple visual proof using slicing and rearranging. Imagine slicing the circle into many equal pieces, like cutting a pizza. The more slices we make, the better our approximation becomes. Now let's rearrange these slices alternately to form a shape that looks almost like a rectangle. As we use more slices, this shape becomes closer to a perfect rectangle. The height of this rectangle is the radius r, and the width is half the circumference, which is pi r. Therefore, the area equals pi r times r, giving us pi r squared. Now let's rearrange these slices alternately to form a shape that looks almost like a rectangle. As we use more slices, this shape becomes closer to a perfect rectangle. If we slice the circle into even more, tiny pieces, and rearrange them, the shape gets closer and closer to a perfect rectangle. Look at this rectangle. Its height is the radius r. Its length is made up of the curved edges of the sectors. Together, these edges form half the circle's circumference. The circumference is two pi r, so half is pi r. The area of a rectangle is length times width, which is pi r times r, giving us pi r squared.