Lesson 9: Applying Area of Circles

Question

A picture of a circle shows 3 circles of different sizes stacked on top of one another. The smallest one which is at the top has an area of  28.27 inches. The middle circle has an area of 63.62 inches. And the bottom circle has an area of 113.1 inches. The total area is 504 inches squared. What is the area of the shaded area?

Answer 1

Please post only one copy of the problem.

I have already addressed the problem and a diagram is needed

to show the locations and the circles and the shaded region

whose area needs to be calculated.

 

Answer 2

Well, we have no picture nor a description, so we do not know what area is shaded.

 

The best we can do is find the radius of each circle.

 

Area = pi * radius^2

 

Area/pi = radius^2

 

So the radius = sqrt( Area/pi)

Note that it is only the positive square root because the radius cannot be negative.

 

The smallest circle then has radius just over 3 inches.

 

The middle circle has radius just under 4.5 inches.

 

The largest circle has radius just over 6 inches.

 

The total of these three circles is almost 205, not 504.

So there must be a square, rectangle, or some other polygon

that contains these circles that is not mentioned here.