Question

Can you please help me, I got some of it wrong but not sure what

Answer 1

It is required to find the area of the sector AOB in terms of π.

Notice that the central angle is 120º.

Recall that the Area of a sector is given as:

`A=(\theta)/(360^(\circ))*\pi r^2`

Where θ is the central angle and r is the radius.

Substitute θ=120º and r=9 into the formula:

`\begin{gathered} A=(120^(\circ))/(360^(\circ))*\pi(9^2) \\ \end{gathered}`

Evaluate the expression on the right:

`A=\frac{\cancel{120^(\circ)}1}{\cancel{360^(\circ)}3}*81\pi=(1)/(3)*81\pi=27\pi\text{ square units}`

Hence, the required area of the sector in terms of π is 27π.