Question

a ring - shaped region is shown below. its inner diameter is 18 yd. the width of the ring is 3 yd. find the area of the shaded region. use 3.14 for π. do not round your answer. yd²

Explanation:

Step1: Calculate inner radius

Inner radius $r = \frac{18}{2} = 9$ yd

Step2: Calculate outer radius

Outer radius $R = 9 + 3 = 12$ yd

Step3: Compute area of outer circle

Area of outer circle $A_o = \pi R^2 = 3.14 \times 12^2 = 3.14 \times 144 = 452.16$ yd²

Step4: Compute area of inner circle

Area of inner circle $A_i = \pi r^2 = 3.14 \times 9^2 = 3.14 \times 81 = 254.34$ yd²

Step5: Find shaded area (difference)

Shaded area $A = A_o - A_i = 452.16 - 254.34$

Answer:

$197.82$ yd²