Question

both circles have the same center. what is the area of the shaded region?
d=35 km
8.3 km
write your answer as a whole number or a decimal rounded to the nearest hundredth.
____ square kilometers

Explanation:

Step1: Find inner circle radius

The diameter of the inner circle is 35 km, so radius $r_{inner} = \frac{35}{2} = 17.5$ km

Step2: Find outer circle radius

Add the width of the shaded ring to the inner radius: $r_{outer} = 17.5 + 8.3 = 25.8$ km

Step3: Calculate area of outer circle

Use the circle area formula $A = \pi r^2$:
$A_{outer} = \pi (25.8)^2 = 665.64\pi$

Step4: Calculate area of inner circle

$A_{inner} = \pi (17.5)^2 = 306.25\pi$

Step5: Find shaded area (difference)

Subtract inner area from outer area:
$A_{shaded} = 665.64\pi - 306.25\pi = 359.39\pi$
Calculate the numerical value: $359.39 \times 3.1416 \approx 1129.16$

Answer:

1129.16 square kilometers