A

Step 1: Radius of the bigger circle = 8 cm and the radius of the smaller circle = 3 cm.

Step 2: Area of the bigger circle = π x (radius of the bigger circle)² [Formula.]

Step 3: [Substitute the value of the radius.] = 3.14 x 8²

Step 4: [Expand 8² as 8 x 8.] = 3.14 x 8 x 8

Step 5: [Multiply.]= 200.96 cm²

Step 6: Area of the bigger circle = 200.96 cm².

Step 7: Area of the smaller circle = π x (radius of the smaller circle)²[Formula.]

Step 8: [Substitute the radius of the smaller circle.] = 3.14 x 3²

Step 9: [Expand 3² as 3 x 3.] = 3.14 x 3 x 3

Step 10: [Multiply.]= 28.26 cm²

Step 11: Area of the smaller circle = 28.26 cm²

Step 12: Area of the shaded region = area of the bigger circle – area of the smaller circle.

Step 13: [Substitute the values.] = 200.96 - 28.26

Step 14: [Subtract.]= 172.7

Step 15: So, area of the shaded region is 172.7 cm².