Final answer:
In mathematics, scaling up an object results in an increased surface area, while scaling down decreases the surface area. The larger a geometric object is, the greater its surface area will be compared to a smaller object of the same shape.
Step-by-step explanation:
The question provided requires an understanding of how scaling affects the surface area of geometric shapes. In mathematics, especially geometry, when an object is scaled, the dimensions of the object are changed by a certain factor. The surface area of a three-dimensional object is the total area of all the surfaces of the object. If the scaling factor is greater than 1, the object increases in size, and thus its surface area also increases. Conversely, if the scaling factor is less than 1, the object decreases in size, reducing its surface area.
When comparing two shapes, if they have different sizes but the same shape, the larger object will typically have a larger surface area. For example, consider two cubes: one with a side length of 1 cm and another with a side length of 3 cm. The smaller cube has a surface area calculated as 6 cm², while the larger cube's surface area is 54 cm². This illustrates that the larger cube has a significantly greater surface area than the smaller cube, despite having the same shape. This principle applies to other shapes like spheres and prisms as well.