Question

find the diameter of each circle. 17) area = 4π in²

Explanation:

Step1: Recall the area formula of a circle

The area formula of a circle is \( A=\pi r^{2} \), where \( A \) is the area and \( r \) is the radius. Given that \( A = 4\pi\space\text{in}^2 \), we substitute it into the formula:
\( 4\pi=\pi r^{2} \)

Step2: Solve for the radius \( r \)

Divide both sides of the equation \( 4\pi=\pi r^{2} \) by \( \pi \):
\( \frac{4\pi}{\pi}=\frac{\pi r^{2}}{\pi} \)
Simplify to get \( 4 = r^{2} \). Then take the square root of both sides:
\( r=\sqrt{4}=2\space\text{in} \) (we take the positive root since radius is a non - negative quantity)

Step3: Find the diameter \( d \)

The relationship between diameter and radius is \( d = 2r \). Substitute \( r = 2\space\text{in} \) into this formula:
\( d=2\times2 = 4\space\text{in} \)

Answer:

The diameter of the circle is \( 4\space\text{in} \)