Chapter 4, Problem 17RE

To determine

Tofind:the area of sector of a circle of radius $\text{18}$ inches and central angle ${\text{θ=120}}^{\text{0}}$

Answer to Problem 17RE

The area of the sector is $339.292$ square inches.

Explanation of Solution

Given:A circle has radius of $\text{18}$ inches and central angle ${\text{120}}^0$

Concept used:

the area of a sector is,

  $\text{A=}\frac{\text{1}}{\text{2}}{\text{r}}^{\text{2}}\text{θ}$

Trigonometric formula:

  ${\text{πradian=180}}^{\text{0}}$

  $\text{1radian=}\frac{{\text{180}}^{\text{0}}}{\text{π}}$

or

  $1^0=1\left(\frac{\pi }{180}\right)\text{radians}$

Calculation:

Let’s consider that a circle has radius of $\text{18}$ inches and central angle ${\text{120}}^0$

Let’s first convert degree measure into radian measure, thus

  ${120}^{{}^0}=120\left(\frac{\pi }{180}\right)$

  $\Rightarrow \frac{2\pi }{3}$

As the area of a sector is,

  $\text{A=}\frac{\text{1}}{\text{2}}{\text{r}}^{\text{2}}\text{θ}$

Therefore get:

  $\text{A=}\frac{1}{2}{\left(18\right)}^2\left(\frac{2\pi }{3}\right)$

  $\Rightarrow 339.292$ square inches.

Hence, The area of the sector is $339.292$ square inches.