Question

What is the area of the shaded region to the nearest tenth?

Answer 1

Answer:

15.1

Step-by-step explanation:

We know that the area of the circle is $\pi r^{2}$, but we are looking for the portion of the circle, this means we multiply it by the portion of the circle that is shaded.

Area of shaded region = $\pi r^{2} (\frac{x}{360} )$

where r = 4 and x = 108, the 360 comes from the fact that the total degrees around the circle is 360, so dividing the total amount of degrees by the angle will give us the portion we are looking for.

Area of shaded region = $\frac{108}{360} \pi 4^{2}$ = 15.1

Another way to think about it is that the area of the total circle is $\pi r^{2}$, multiplying it by a fraction, a number less than 1, would give us a smaller value.

Hope this helps.