Final answer:
The statement is true; the increase in the area of a circular plate when the radius increases can be approximated using differentials, which is a concept from calculus used to estimate small changes.
Step-by-step explanation:
When the radius of a circular plate increases from 10 cm to 10.1 cm, the increase in the area of the top surface can indeed be approximated using differentials. This statement is true. To understand why, let's consider the formula for the area of a circle, which is A = π r^2, where A is the area and r is the radius of the circle. When we take a differential of this formula, dA, which represents the change in area with respect to the change in radius (dr), we get dA = 2π r dr. For a small change in radius, differential approximation provides a quick way to estimate the change in area.