Question

the area of a circle is 2.0096 square centimeters. what is the circles radius? round your answer to the nearest hundredth. centimeters

Explanation:

Step1: Recall the area formula of a circle

The area \( A \) of a circle is given by the formula \( A=\pi r^{2} \), where \( r \) is the radius of the circle. We know \( A = 2.0096\) square centimeters and we need to find \( r \). So we can rearrange the formula to solve for \( r \): \( r=\sqrt{\frac{A}{\pi}} \).

Step2: Substitute the value of \( A \) into the formula

Substitute \( A = 2.0096\) and \( \pi\approx3.14 \) into the formula \( r=\sqrt{\frac{A}{\pi}} \). First, calculate \( \frac{A}{\pi} \): \( \frac{2.0096}{3.14}=0.64 \).

Step3: Take the square root of the result

Now, find the square root of \( 0.64 \). We know that \( \sqrt{0.64} = 0.8 \) because \( 0.8\times0.8 = 0.64 \).

Answer:

\( 0.80 \) (rounded to the nearest hundredth, since \( 0.8 \) is already to the tenths place, but when rounded to the nearest hundredth, it is \( 0.80 \))