Amy marks two points A and B that are 4 inches apart. She draws one circle that has segment AB as a diameter. She then draws a larger circle, which overlaps the first circle, such that the arc from A to B along its circumference is a quarter-circle. What is the total area covered by the two circles? Express your answer in terms of m.

Answer 1

The radius of the smaller circle is half the length of AB, so it is 2 inches.
The circumference of the smaller circle is 2π times the radius, so it is 4π inches.
The larger circle has a quarter-circle arc of AB, so its total circumference is four times longer than the circumference of the smaller circle, so it is 16π inches.
Divide the circumference by 2π to find the diameter is 8 inches.
So, the radius of the larger circle is half the diameter, or 4 inches.
The area of a circle is πr², so the area of the smaller circle is π(2²) = 4π square inches.
The area of the larger circle is π(4²) = 16π square inches.
The total area covered by the two circles is 4π + 16π = <<4+16=20>>20π square inches. Answer: \boxed{20\pi}.