Question

a ring - shaped region is shown below. its inner radius is 14 cm, and its outer radius is 17 cm. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Recall annulus area formula

The area of a ring (annulus) is $\text{Area} = \pi(R^2 - r^2)$, where $R$ is outer radius, $r$ is inner radius.

Step2: Substitute given values

$R=17$, $r=14$, $\pi=3.14$
$\text{Area} = 3.14\times(17^2 - 14^2)$

Step3: Calculate squared radii

$17^2=289$, $14^2=196$
$\text{Area} = 3.14\times(289 - 196)$

Step4: Compute difference inside parentheses

$289-196=93$
$\text{Area} = 3.14\times93$

Step5: Final multiplication

$3.14\times93=292.02$

Answer:

292.02 $\text{cm}^2$