To solve the problem, we need to understand the given expression and interpret what each factor represents.
The given expression for the total mass of the paperweight is:
[tex]\[ 3.14 h^3 - 25.12 h^2 + 50.24 h \][/tex]
Let's focus on interpreting the factor [tex]\(3.14(h-4)^2\)[/tex].
We know that [tex]\(3.14\)[/tex] is an approximation of the mathematical constant [tex]\(\pi\)[/tex], which is commonly used in geometry to calculate areas and volumes involving circles and spheres.
Given the context of the problem, which involves a cone-shaped paperweight, let's consider what [tex]\( (h-4)^2 \)[/tex] might represent within this framework.
For a cone, the area of the base is calculated by the formula:
[tex]\[ \text{Area} = \pi r^2 \][/tex]
where [tex]\( r \)[/tex] is the radius of the base.
Given the factor [tex]\( 3.14(h-4)^2 \)[/tex], we can compare this to the formula for the area of the base of a cone:
[tex]\[ 3.14 \times (\text{radius})^2 \][/tex]
To interpret [tex]\( (h-4) \)[/tex], consider that it is most likely representing the radius of the base of the cone. Thus,
[tex]\[ 3.14(h-4)^2 \][/tex]
fits the form of [tex]\(\pi r^2 \)[/tex], which is indeed the area of the circular base of the paperweight.
Therefore, the best interpretation of the factor [tex]\( 3.14(h-4)^2 \)[/tex] is:
D. the area of the base of the paperweight.
