Let's explore the formula for the area of a circle to determine what gets multiplied by [tex]\(\pi\)[/tex].
The standard formula for the area of a circle is:
[tex]\[
A = \pi r^2
\][/tex]
In this formula:
- [tex]\( A \)[/tex] represents the area of the circle.
- [tex]\( \pi \)[/tex] (pi) is a mathematical constant approximately equal to 3.14159.
- [tex]\( r \)[/tex] is the radius of the circle.
Now, let's analyze the options provided:
A. [tex]\( r^2 \)[/tex]: In the formula [tex]\( A = \pi r^2 \)[/tex], the radius squared ([tex]\( r^2 \)[/tex]) is multiplied by [tex]\(\pi\)[/tex]. This aligns exactly with the formula we're using.
B. [tex]\( d^2 \)[/tex]: [tex]\( d \)[/tex] is the diameter of the circle. The area formula does not involve [tex]\( d^2 \)[/tex]; hence, this option is incorrect.
C. [tex]\( d \)[/tex]: While the diameter ([tex]\( d \)[/tex]) is related to the radius ([tex]\( r = \frac{d}{2} \)[/tex]), the area formula involves [tex]\( r^2 \)[/tex], not just the diameter ([tex]\( d \)[/tex]). Therefore, this option is also incorrect.
D. [tex]\( r \)[/tex]: The radius [tex]\( r \)[/tex] by itself is not directly multiplied by [tex]\(\pi\)[/tex] for the area formula—we need [tex]\( r^2 \)[/tex]. So this option is likewise incorrect.
Therefore, the part of the formula for the area of a circle that gets multiplied by [tex]\(\pi\)[/tex] is:
[tex]\[
\boxed{r^2}
\][/tex]
So, the correct answer is:
A. [tex]\( r^2 \)[/tex], which corresponds to option [tex]\(1\)[/tex].
