Final answer:
The area of the shaded region between two concentric circles, with radii of 6 cm and 9 cm, is found by subtracting the area of the smaller circle from that of the larger circle. It equals 45π cm² or approximately 141.37 cm² if π is approximated as 3.14159.
Step-by-step explanation:
To calculate the area of the shaded region between two concentric circles, we subtract the area of the smaller circle from the area of the larger circle. The formula for the area of a circle is A = πr², where π is approximately 3.14159 and b is the radius of the circle.
The area of the larger circle with a radius of 9 cm is A_large = π * 9² cm² = π * 81 cm². The area of the smaller circle with a radius of 6 cm is A_small = π * 6² cm² = π * 36 cm².
To find the shaded region, we calculate:
Shaded Area = A_large - A_small
= (π * 81 cm²) - (π * 36 cm²)
= π * (81 cm² - 36 cm²)
= π * 45 cm²
Therefore, the area of the shaded region is 45π cm², which is an exact representation. If we use the approximate value of π (3.14159), the numerical approximation would be 141.37 cm², but we often leave the answer in terms of π unless otherwise specified.