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 area formula for a circle

The area of a circle is $A = \pi r^{2}$, where $r$ is the radius.

Step2: Calculate outer - circle area

The outer - radius $R = 17$ cm. So the area of the outer circle $A_{1}=\pi R^{2}=3.14\times17^{2}=3.14\times289$.

Step3: Calculate inner - circle area

The inner - radius $r = 14$ cm. So the area of the inner circle $A_{2}=\pi r^{2}=3.14\times14^{2}=3.14\times196$.

Step4: Calculate the area of the shaded region

The area of the shaded region $A = A_{1}-A_{2}=3.14\times(289 - 196)=3.14\times93$.
$A=292.02$

Answer:

$292.02$