Question

determine the measure of each of the following. a. Arc length of AE b. Arc length of DB c. Area of sector DCB d. Area of shaded region of sector BD

Answer 1

Solution:

Given the figure below:

A) Arc length of AE.

Thus, we have the length of the arc AE to be

$\begin{gathered} length\text{ or arc AE=}\frac{130}{360}\times2\times\pi\times5 \\ =11.34464\text{ inches} \end{gathered}$

B) Arc length of DB

The length of the arc DB is evaluated as

$\begin{gathered} length\text{ of arc DB=}\frac{130}{360}\times2\times\pi\times7 \\ =15.88249\text{ inches} \end{gathered}$

C) Area of sector DCB

The area of the sector DCB is evaluated as

$\begin{gathered} area\text{ of sector DFB=}\frac{130}{360}\times\pi\times7\times7 \\ =55.58873\text{ square inches} \end{gathered}$

D) Area of shaded region of sector BD

The area of the shaded region is expressed as

$area\text{ of big circle - area of small circle}$

Thus, we have the area of the shaded region to be

$\begin{gathered} area\text{ of shaded region = \lparen}\pi\times7\times7)-(\pi\times5\times5) \\ =49\pi-25\pi \\ =24\pi \\ =75.39822\text{ square inches} \end{gathered}$