Question

The radius of a circle is 6 centimeters. What is the area of a sector bounded by a 150 degree arc?Give the exact answer in simplest form._____ square centimeters

Answer 1

Concept

`\text{Area of a sector = }(\theta)/(360)\text{ }*\text{ }\pi r^2`
`\begin{gathered} \theta\text{ is the angle subtend at the center} \\ r\text{ is the radius} \end{gathered}`

Step 1: List the given data

`\begin{gathered} \theta=150^o \\ r\text{ = 6cm} \\ \pi\text{ = }(22)/(7) \end{gathered}`

Step 2: Substitute the values to find the area of the sector.

`\begin{gathered} \text{Area of the sector = }(150)/(360)\text{ }\pi\text{ }*6^2 \\ =\text{ }\frac{150\text{ }\pi\text{x 36}}{360\text{ }} \\ =15cm^2 \end{gathered}`

Ok