Question

a ring - shaped region is shown below. its inner radius is 11 in, and its outer radius is 17 in. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Recall the area formula for a circle

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

Step2: Calculate the area of the outer - circle

The outer - radius $R = 17$ in. So the area of the outer - circle $A_{1}=\pi R^{2}=3.14\times17^{2}=3.14\times289 = 907.46$ in².

Step3: Calculate the area of the inner - circle

The inner - radius $r = 11$ in. So the area of the inner - circle $A_{2}=\pi r^{2}=3.14\times11^{2}=3.14\times121 = 379.94$ in².

Step4: Calculate the area of the shaded region

The area of the shaded region (the area of the ring) is $A = A_{1}-A_{2}$. So $A=907.46 - 379.94=527.52$ in².

Answer:

$527.52$ in²