Answer:
308 square inches
Step-by-step explanation:
See the image I posted.
First, you need to know that the B is the center of the large circle.
Here's why:
Draw a tangent line DE that passes through the intersection of the large circle and either of the small circle (I chose the right one).
This tangent line is perpendicular to the diameter CB of the small circle.
The fact that CB is perpendicular to DE makes the length CB equal to the radius of the large circle because radius is perpendicular to tangent at the point of contact.
So, CB is the radius of large circle and CB = 14 inches.
We can find out the area of large circle using formula:
[tex]\text{Area of circle = }\pi R^2[/tex]
[tex]\text{or, }A=\pi (14)^2\\[/tex]
[tex]\text{or, }A=196\pi[/tex]
Now the radius of a small circle is already given 7 inches, so the area of two circles is:
[tex]a=\pi r^2+\pi r^2\\[/tex]
[tex]\text{or, }a=2\pi (7)^2\\[/tex]
[tex]\text{or, }a=98\pi[/tex]
Finally, the shaded region will be equal to the difference of area of large circle and the area of two small circles.
[tex]\text{Area of shaded region = }A-a=196\pi-98\pi=98\pi=307.876\approx308\ \text{sq. inches}[/tex]
