Question

What is the area of a sector of a circle with a central angle of measure 30° and whose diameter is 6 cm? Leave your answer in terms of π.

Answer 1

The Solution:

Given:

`\begin{gathered} central\text{ angle of a sector}=\theta=30^o \\ \\ diameter=6cm \\ \\ r=radius=(6)/(2)=3cm \end{gathered}`

Required:

Find the area of a sector.

The formula for area:

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

Substitute:

`Area=(30)/(360)*\pi(3)^2=(\pi)/(2)cm^2`

Answer:

`(\pi)/(2)cm^2\text{ or }0.5\pi cm^2`