Question

Please assist me in finding the area of the ShADED sector or segment

Answer 1

Step 1:

In this question, we are given the following:

Finding the area of the shaded sector or segment:

Step 2:

The details of the solution are as follows:

Recall that the area of the circle =

`\begin{gathered} \pi r^2 \\ Now,\text{ the radius of the Big circle = 7} \\ Th\text{e radius of the smallest circle = 1} \\ Then,\text{ the radius of the middle circle = \lparen}(7-1)/(2))\text{ + 1 = 3 + 1 = 4} \end{gathered}`

`Area\text{ of the shaded sector = }\pi\text{ \lparen7 \rparen}^2\text{ - }\pi\text{ \lparen4\rparen}^2\text{ + }\pi\text{ \lparen1 \rparen}^2`
`\begin{gathered} Area\text{ of the shaded sector = 49}\pi\text{ -16}\pi\text{ +}\pi\text{ =34}\pi\text{ = 106 . 8141502} \\ \approx\text{ 106 . 8 cm}^2\text{ \lparen correct to one decimal place \rparen} \\ \\ \end{gathered}`

CONCLUSION:

The area of the shaded sector or segment =

`106.\text{ 8 cm}^2\text{ \lparen correct to one decimal place \rparen}`