This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
Step 1: Identify the radii of the inner and outer circles. The radius of the inner circle is given as r_1 = 2.5 cm. The width of the shaded region is 1 cm. The radius of the outer circle is the sum of the inner radius and the width of the shaded region. r_2 = r_1 + 1 cm = 2.5 cm + 1 cm = 3.5 cm Step 2: Calculate the area of the inner circle. The formula for the area of a circle is A = r^2. A_1 = r_1^2 = (2.5 cm)^2 = 6.25 cm^2 Step 3: Calculate the area of the outer circle. A_2 = r_2^2 = (3.5 cm)^2 = 12.25 cm^2 Step 4: Calculate the area of the shaded part. The area of the shaded part is the difference between the area of the outer circle and the area of the inner circle. A_shaded = A_2 - A_1 A_shaded = 12.25 cm^2 - 6.25 cm^2 A_shaded = (12.25 - 6.25) cm^2 A_shaded = 6 cm^2 The area of the shaded part is 6 cm^2.