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: $r = \square$

a circle with an area of 78.5 square centimeters has a radius of $\square$ centimeters.

Explanation:

Step1: Solve for \( r \) from \( A = \pi r^2 \)

We start with the formula \( A=\pi r^{2} \). To solve for \( r \), first divide both sides by \( \pi \):
\( \frac{A}{\pi}=r^{2} \)
Then take the square root of both sides. Since the radius is a non - negative quantity, we have \( r = \sqrt{\frac{A}{\pi}} \) (we consider the positive square root as radius cannot be negative).

Step2: Calculate the radius when \( A = 78.5 \) and \( \pi=3.14 \)

Substitute \( A = 78.5 \) and \( \pi = 3.14 \) into the formula \( r=\sqrt{\frac{A}{\pi}} \).
First, calculate \( \frac{A}{\pi} \): \( \frac{78.5}{3.14}=25 \)
Then, take the square root of 25: \( r=\sqrt{25} = 5 \)

Answer:

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