Question

4.26. use the formula for the area of a circle to solve for the radius of the circle if the area is 78.5 cm².

Explanation:

Step1: Write the formula for the area of a circle

The formula for the area of a circle is \(A=\pi r^{2}\), where \(A\) is the area and \(r\) is the radius. Given \(A = 78.5\space cm^{2}\) and taking \(\pi=3.14\).

Step2: Solve for \(r^{2}\)

Substitute the values into the formula: \(78.5 = 3.14r^{2}\). Then, \(r^{2}=\frac{78.5}{3.14}\).

$$r^{2}=\frac{78.5}{3.14}=25$$

Step3: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius is a non - negative quantity), \(r = \sqrt{25}\).

Answer:

\(r = 5\space cm\)