To determine the correct algebraic representation for the area of a circle, let's analyze each of the given options in detail:
1. Option (A): Area [tex]\(= \pi r\)[/tex]
- This formula does not correctly represent the area of a circle. [tex]\(\pi r\)[/tex] would suggest a linear relationship, but area calculations involve squaring the radius.
2. Option (B): Area [tex]\(= \pi r^2\)[/tex]
- This formula is the correct representation for the area of a circle. It correctly incorporates the radius squared, showing that the area grows with the square of the radius.
3. Option (C): Area [tex]\(= \pi d\)[/tex]
- This formula also does not correctly represent the area of a circle. [tex]\(\pi d\)[/tex] would similarly suggest a linear relationship and does not square a relevant dimension.
4. Option (D): Area [tex]\(= \pi d^2\)[/tex]
- This formula incorrectly uses the diameter squared instead of the radius squared. The correct formula involves the square of the radius (half of the diameter), not the diameter itself.
Given these details, the correct answer is:
(B) Area [tex]\(= \pi r^2\)[/tex].
