Geometry: shaded region formed by smaller circle being removed from larger circle; area is 64pi; smaller radius is 6

amp1053

New member
I’m really unsure of how to do this problem and need some help. The image shows a large shaded circle with a smaller unshaded circle inside. It reads, "This figure consists of 2 concentric circles. If the shaded area is 64 (pi) sq. in. and the smaller circle has a radius of 6 in., what is the radius, in inches of the larger circle?" I wasn’t at school today and I have a little work done (as shown in the photo), but I’m really struggling and I have no clue what to do. Thanks for the help!! Attachments

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Dr.Peterson

Elite Member
You've found that the inner circle has an area of $$\displaystyle 36\pi$$ sq. in. What is the area of the outer circle (including shaded and unshaded parts)? What radius would give that area? (Note that it's better not to calculate decimal values for a problem like this, since they gave you the shaded area in terms of pi.)

amp1053

New member
So I added the areas to get a total area of 100 sq. in., but I am lost on how to find a radius for this area. I’m sorry that I’m asking so many questions.

• Harry_the_cat

Dr.Peterson

Elite Member

First, don't forget the pi! You're adding $$\displaystyle 36\pi + 64\pi = 100\pi$$, not just 100.

Suppose I gave you this problem:

If a circle's area is $$\displaystyle 100\pi$$ sq. in., what is its radius?​

You would, I hope, write an equation that expresses this fact, and try to solve it. What is the formula for the area of a circle?

Harry_the_cat

Senior Member
Almost. $$\displaystyle 36\pi +64\pi = 100 \pi$$ square inches.

Next step: Write down the formula for the area of a circle in terms of r. Let this equal $$\displaystyle 100\pi$$ and solve for r.

Snap, Dr P.