Question

a ring - shaped region is shown below. its inner radius is 17 cm. the width of the ring is 4 cm. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Find the outer radius

The inner radius \( r = 17\) cm and the width of the ring is \(4\) cm. So the outer radius \( R=r + 4=17 + 4=21\) cm.

Step2: Use the formula for the area of a ring

The area of a ring (annulus) is \(A=\pi(R^{2}-r^{2})\). Substitute \(R = 21\), \(r = 17\), and \(\pi=3.14\) into the formula.
First, calculate \(R^{2}-r^{2}\):

$$
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$$

Then, calculate \(A\):
\(A = 3.14\times152\)

Step3: Calculate the final result

\(A=3.14\times152 = 477.28\)

Answer:

\(477.28\)