Problem
# 13
In this diagram, the smaller circles touch the larger circle and touch each other at the center of the larger circle. The radius of the larger circle is 6. What is the area of the shaded region? (look at page to see diagram)
Solution
First you find the area of the big circle. The formula to do so is πr².
This would appear like π6² = 36π
(You would put 36π instead of the expanded form because it's exact)
Now you find the area to one of the smaller circles inscribed in the the larger circle.
You use the same formula πr² which results in π3²
(We use 3 because the radius is half of the larger circles radius)
π3² = 9π(2) = 18π
(You would multiply 9π by two because there are two circles inscribed in the larger circle)
The final step is to subtract 18π from 36π. This would look like 36π - 18π = 18π
The area of the shaded area is 18π
Why do you like this question?
I like this question because it involves circles and I enjoy finding they're area. It was as well very simple to find out and it gives me more practice using exact answers.
What have you learned about the process of problem solving?
I've learned that I shouldn't round my answer till the last step. I sometimes do this without noticing but I'm breaking out of this habit.
