To determine what gets multiplied by [tex]\(\pi\)[/tex] in the formula for the area of a circle, we'll review the formula for the area of a circle. The standard formula for the area [tex]\(A\)[/tex] of a circle is:
[tex]\[ A = \pi r^2 \][/tex]
Here, [tex]\(r\)[/tex] represents the radius of the circle.
Let's consider each option given in the question:
- Option A: [tex]\(d\)[/tex]
[tex]\(d\)[/tex] stands for the diameter of the circle. The formula for the area of a circle does not use the diameter directly; it uses the radius [tex]\(r\)[/tex]. Hence, [tex]\(d\)[/tex] is not correct.
- Option B: 5
The number 5 is arbitrary and has no direct relevance to the formula for the area of a circle. Therefore, 5 is not correct.
- Option C: [tex]\(d^2\)[/tex]
[tex]\(d^2\)[/tex] would represent the square of the diameter of the circle. This is not part of the standard formula for the area of a circle, so [tex]\(d^2\)[/tex] is not correct.
- Option D: [tex]\(r^2\)[/tex]
[tex]\(r^2\)[/tex] represents the square of the radius of the circle, which is exactly what is used in the formula [tex]\(A = \pi r^2\)[/tex].
Therefore, the correct answer is:
D. [tex]\(r^2\)[/tex]
