Question

both circles have the same center. what is the area of the shaded region?
write your answer as a whole number or a decimal rounded to the nearest hundredth.
square centimeters

Explanation:

Step1: Find inner circle radius

The diameter of the inner circle is $d=74.2$ cm, so radius $r_{inner} = \frac{74.2}{2} = 37.1$ cm

Step2: Find outer circle radius

The width of the shaded region is 56.4 cm, so $r_{outer} = 37.1 + 56.4 = 93.5$ cm

Step3: Calculate inner circle area

Use area formula $A=\pi r^2$:
$A_{inner} = \pi (37.1)^2 = \pi \times 1376.41 \approx 4324.21$ cm²

Step4: Calculate outer circle area

$A_{outer} = \pi (93.5)^2 = \pi \times 8742.25 \approx 27463.22$ cm²

Step5: Find shaded region area

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

Answer:

23139.01 square centimeters