Question

37. Solve for the area of the shaded sector below, given the radius is 9 cm.

Answer 1

To solve this problem, we will use the following formula for the area of a sector:

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

where θ is the central angle, and r is the radius.

From the given data, we know that:

`\begin{gathered} \theta=360^(\circ)-120^(\circ)=240^(\circ), \\ r=9cm. \end{gathered}`

Therefore,

`A=(240^(\circ))/(360^(\circ))\pi(9cm)^2.`

Computing the value of A, we get:

`A=54\pi\text{ cm}^2.`

Answer:

`\begin{equation*} 54\pi\text{ cm}^2. \end{equation*}`