To arrive at an interpretation of the factor [tex]\(3.14(h - 4)^2\)[/tex], let's consider each provided option and analyze whether it matches the expression [tex]\(3.14(h - 4)^2\)[/tex].
### Step-by-Step Explanation:
1. Given Expression:
The factor given in the expression is [tex]\(3.14(h - 4)^2\)[/tex].
2. Interpretation of the Factor:
The number [tex]\(3.14\)[/tex] is being used as an approximation for [tex]\(\pi\)[/tex], which is commonly involved in formulas related to circles and circular bases in geometrical shapes like cones.
3. Form of the Factor:
The expression [tex]\((h - 4)^2\)[/tex] suggests that it is representing a square of a linear dimension. When multiplied by [tex]\(3.14\)[/tex], it gives us:
[tex]\[
\text{Area} = \pi \times (h - 4)^2
\][/tex]
This form aligns with the formula for the area of a circle, [tex]\(\pi r^2\)[/tex], where [tex]\(r\)[/tex] would be the radius of the circular base.
4. Analyzing the Options:
- A. the area of the base of the paperweight:
The base of a cone is circular and its area is computed using [tex]\(\pi r^2\)[/tex]. Given [tex]\(3.14(h - 4)^2\)[/tex], it appears to be expressing the area of the circular base.
- B. the surface area of the paperweight:
The surface area of a cone includes the lateral surface area and possibly other components, not just [tex]\((h - 4)^2\)[/tex].
- C. the area of the photo attached to the base of the paperweight:
The photo is described as being square, whereas our factor involves [tex]\(\pi\)[/tex], suggesting a circular area rather than a square.
- D. the lateral area of the paperweight:
The lateral area of a cone is different from the base area and would involve [tex]\(\pi\)[/tex], the radius, and the slant height, not [tex]\((h - 4)^2\)[/tex].
### Conclusion:
Among the options given, the expression [tex]\(3.14(h - 4)^2\)[/tex] is best interpreted as the area of the base of the paperweight, which is option A.
Thus, the best interpretation of the factor [tex]\(3.14(h-4)^2\)[/tex] is:
A. the area of the base of the paperweight.
