We can begin to work this problem by using the radius to find the area of each smaller circle, finding the full area of the larger circle, subtracting it by the area of a smaller circle x the amount of circles, then dividing by six (because if you look closely, you can see there are 6 figures just like the one colored in).
First, finding the area of a smaller circle.
The area of a circle is πr^2.
So, it would be π(5)^2.
Or, 25π (~78.54)
Now that we know the area of one circle, we can find the area all of the circles take up by multiplying the area by 7.
175π (Keep this number in mind.)
Next, we need to find the area of the bigger circle.
Notice there are three circles that can act as the diameter of the larger circle.
We can use this to help us find the area.
We know each circle has a diameter of 10 (since the radius is 5).
The three circles added end up being 30, so, the diameter of the larger circle is 30.
Let's find the area (π(5)^2).
R = radius (15)
π(15)^2 = 225π...
...is the area of the larger circle.
Next, we can subtract all of the smaller circles out. Remember that number I asked you to keep in mind? This is where it will come into play.
225 π (total area of the larger circle - 175π (all of the smaller circles area combined) = 50π
However, this is the area of ALL of the leftovers from the smaller circles.
We need to divide this by 6 to find how big each section identical to the shaded area is.
50 ÷ 6 = 8.3333333...(or 8.33 for short)
I believe the area of the shaded part of the circle is 8.33π.
However, I may be incorrect! If your teacher/instructor has taught you a specific process of how to complete this problem, please consider checking my answer or attempting to perform the math.
Hope I could help you out! If my answer is incorrect, or it isn't the answer you were looking for, please let me know! However, if my answer was correct and my explanations were easy to comprehend, please consider marking my answer as Brainliest.
Have a good one!
God bless.
