Final answer:
The area of the lune is found by subtracting the area of the smaller circle from that of the larger circle, leading to a formula A = π(r2² - r1²). None of the options provided accurately represent this formula.
Step-by-step explanation:
To find the area of the crescent-shaped region (called a lune) bounded by arcs of circles with radii r1 and r2, where r2 is greater than r1, we will use the formula for the area of a circle A = πr², where π is approximately 3.14159. Since the lune is essentially the difference between the two circles, the area of the larger circle with radius r2 is πr2² and the area of the smaller circle with radius r1 is πr1². Subtracting the area of the smaller circle from that of the larger circle gives us A = πr2² - πr1² = π(r2² - r1²).
After simplifying the equation, we see that none of the offered options directly match our formula. However, option b) A=π(r2-r1)² is very close but incorrectly implies the subtraction of the radii first before squaring. The correct form should maintain the squares of the radii in the subtraction. So, the correct form would be A = π(r2² - r1²), which is not listed among the options.