Question

a ring - shaped region is shown below. its inner diameter is 16 in. the width of the ring is 4 in. find the area of the shaded region. use 3.14 for π. do not round your answer.

Explanation:

Step1: Calculate inner - radius

The inner - diameter $d = 16$ in, so the inner - radius $r=\frac{d}{2}=\frac{16}{2}=8$ in.

Step2: Calculate outer - radius

The width of the ring is 4 in. So the outer - radius $R=r + 4=8 + 4=12$ in.

Step3: Calculate the area of the shaded region

The area of a circle is $A=\pi R^{2}-\pi r^{2}=\pi(R^{2}-r^{2})$. Substitute $R = 12$ in, $r = 8$ in and $\pi=3.14$. Then $A = 3.14\times(12^{2}-8^{2})=3.14\times(144 - 64)=3.14\times80$.

Answer:

$251.2$ in$^{2}$