Question

both circles have the same center. the circumference of the inner circle is 395.012 meters. what is the area of the shaded region? write your answer as a whole number or a decimal rounded to the nearest hundredth.

Explanation:

Step1: Find inner circle radius

Use $C=2\pi r$, solve for $r$:
$r_{inner} = \frac{C}{2\pi} = \frac{395.012}{2\times3.1416} \approx 62.87$ m

Step2: Find outer circle radius

Add the width to inner radius:
$r_{outer} = 62.87 + 33.8 = 96.67$ m

Step3: Calculate area of outer circle

Use $A=\pi r^2$:
$A_{outer} = \pi\times(96.67)^2 \approx 3.1416\times9345.0889 \approx 29358.5$ m²

Step4: Calculate area of inner circle

Use $A=\pi r^2$:
$A_{inner} = \pi\times(62.87)^2 \approx 3.1416\times3952.6369 \approx 12417.6$ m²

Step5: Find shaded area (difference)

Subtract inner area from outer area:
$A_{shaded} = 29358.5 - 12417.6$

Answer:

16940.9 square meters