Question

both circles have the same center. what is the area of the shaded region?
d=24 mm
26 mm
write your answer as a whole number or a decimal rounded to the nearest hundredth.
square millimeters

Explanation:

Step1: Find radius of inner circle

The diameter of the inner circle is 24 mm, so radius \( r_{inner} = \frac{24}{2} = 12 \) mm.

Step2: Identify radius of outer circle

The radius of the outer circle \( r_{outer} = 26 \) mm.

Step3: Calculate area of shaded region (annulus)

The area of an annulus is \( A = \pi r_{outer}^2 - \pi r_{inner}^2 = \pi (r_{outer}^2 - r_{inner}^2) \).
Substitute values: \( A = \pi (26^2 - 12^2) = \pi (676 - 144) = \pi \times 532 \).
Using \( \pi \approx 3.14159 \), \( A \approx 3.14159 \times 532 \approx 1670.56 \) square millimeters.

Answer:

1670.56