Chapter 12.2, Problem 7MRE

To determine

To find: The radius and circumference of the circle if area is given.

Answer to Problem 7MRE

The radius of the circle is 7 and the circumference of the circle is $14\pi$ .

Explanation of Solution

Given information: The area of the circle is $49\pi$ .

Calculation:

The area of the circle with radius $r$ is given by,

  $A=\pi r^2$

Substitute $49\pi$ for $A$ in the above formula.

  $\begin{array}{c}49\pi =\pi {\left(r\right)}^2\\ r^2=49\\ r=\sqrt{49}\\ =7\end{array}$

The formula of the circumference of a circle with radius $r$ is:

  $C=2\pi r$

Substitute 7 for $r$ in the above formula.

  $\begin{array}{c}C=2\pi \left(7\right)\\ =14\pi \end{array}$

Therefore, the radius of the circle is 7 and the circumference of the circle is $14\pi$ .