Question

a circle has an area of 314 cm². what is its radius? (use π ≈ 3.14 )

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.

Step2: Substitute the given values into the formula

We know that \(A = 314\space cm^{2}\) and \(\pi\approx3.14\). Substituting these values into the formula gives \(314=3.14r^{2}\).

Step3: Solve for \(r^{2}\)

Divide both sides of the equation by \(3.14\): \(\frac{314}{3.14}=r^{2}\). So, \(r^{2} = 100\).

Step4: Solve for \(r\)

Take the square root of both sides. Since \(r>0\) (radius cannot be negative), \(r=\sqrt{100}=10\space cm\).

Answer:

10 cm