Chapter 10 - Area - 10-7 Areas of Circles and Sectors - Practice and Problem-Solving Exercises - Page 663: 10

$\dfrac{\pi}{9} \ in.^2$

Let $A$ be the area of a circle. The area $(A)$ of a circle whose radius is $R$ is given by: $A=\pi r^2 ...(1)$ We know that the radius is half of the diameter of a circle. That is, $r=\dfrac{d}{2}=\dfrac{\frac{2}{3}}{2}=\dfrac{1}{3}$ Plug the data in the equation (1) to obtain: $A=\pi (\dfrac{1}{3})^2=\pi(\dfrac{1}{9})$ Therefore, we get , $Area=\dfrac{\pi}{9} \ in.^2$