Scale Factor and Total Surface Area of a Cylinder

① This example dynamically demonstrates how the total surface area (TSA) of a cylinder changes when its scale factor is adjusted. ② Core mathematical concepts include the surface area formula for a cylinder in solid geometry, properties of similar figures under scaling, and the quadratic relationship between linear scale factor and area. ③ Construction details: The GeoGebra commands Cylinder and Segment are used to create the cylinder and its defining segments (radius and height), with objects a, A, B, b, c, d, e, f, C, g, h, i, j, and text1 serving for measurements, labels, and calculations. ④ Suitable for middle or high school geometry classes or self-study, this interactive tool helps learners visualize how scaling affects surface area, reinforcing spatial reasoning and algebraic connections.