Question

I need help with this question. the last tutor gave me a wrong answerthe last asnwer was 3/2 π

Answer 1

We have the following general rule to find the length of an arc:

`Arc=r\cdot(\alpha\cdot(2\pi))/(360)`

where r is the radius and alpha is the measure of the central angle in degrees.

In this case, we have that r = 8 and alpha equals 270 degrees, since that is the measure of the angle that completes the full circumference, then:

`\begin{gathered} Arc=8\cdot((270\cdot2\pi)/(360))=8\cdot((540)/(360)\pi)=8((3)/(2)\pi)=(24)/(2)\pi=12\pi \\ \Rightarrow Arc=12\pi \end{gathered}`

therefore, the length of the gray arc is 12 pi