Question

the equation shown relates a, the area of a circle, to r, the radius of the circle.
a = \\( \pi r ^ { 2 } \\)
solve the formula for r. then find the radius of a circle that has an area of 78.5 square centimeters. use 3.14 for \\( \pi \\).
enter your answers in the boxes.
formula \\( r = \\)
a circle with an area of 78.5 square centimeters has a radius of centimeters.

Explanation:

Step1: Solve the formula for \( r \)

Given \( A=\pi r^{2} \), divide both sides by \( \pi \): \( \frac{A}{\pi}=r^{2} \). Then take the square - root of both sides: \( r = \sqrt{\frac{A}{\pi}} \).

Step2: Substitute \( A = 78.5 \) and \( \pi=3.14 \) into the formula for \( r \)

First, calculate \( \frac{A}{\pi}=\frac{78.5}{3.14}=25 \). Then, \( r=\sqrt{25} \).

Answer:

Formula \( r=\sqrt{\frac{A}{\pi}} \)
A circle with an area of 78.5 square centimeters has a radius of \( 5 \) centimeters.