Question

a ring - shaped region is shown below. its inner diameter is 30 cm. the width of the ring is 3 cm. find the area of the shaded region. use 3.14 for π. do not round your answer. cm²

Explanation:

Step1: Find inner radius

Inner diameter is 30 cm, so inner radius \( r = \frac{30}{2} = 15 \) cm.

Step2: Find outer radius

Ring width is 3 cm, so outer radius \( R = 15 + 3 = 18 \) cm.

Step3: Calculate area of shaded region

The area of a ring (annulus) is \( A=\pi(R^{2}-r^{2}) \). Substitute \( R = 18 \), \( r = 15 \), and \( \pi = 3.14 \):

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Answer:

\( 310.86 \)