Use the figure below to answer questions 8 through 9.What is the area of the shaded figure?

In question, it is given diameter of smaller circle = 15ft

Now, diameter of smaller circle = Radius of bigger circle = R = 15ft

So, area of the bigger circle = $$\pi\ R^2$$ = $$\pi\ \left(15\right)^2$$ = $$225\pi\ $$ square feet.

Radius of smaller circle = r = R/2 = 15/2 = 7.5ft

So, area of smaller circle = $$\pi\ r^2$$ = $$\pi\ \left(7.5\right)^2$$ square feet.

But there are two smaller circles, so combined area of both the smaller circles = $$2\pi\ \left(7.5\right)^2$$ square feet.

So, area of shaded region = $$225\pi\ -2\pi\ \left(7.5\right)^2$$ = $$225\pi\ -2\pi\ \left(\dfrac{15}{2}\right)^2$$ = $$225\pi\ -2\pi\ \times\ \dfrac{225}{4}=225\pi\ -\dfrac{225\pi}{2}=\dfrac{225\pi}{2}=112.5\pi\ $$ square feet.