Chapter 10.9, Problem 9PSB

a)

To determine

To find : The Length of arc.

Answer to Problem 9PSB

  $4\pi \sqrt{3}$

Explanation of Solution

Given Information :

  

radius of $\stackrel{⌢}{\text{AB}}(r)=\text{OA}$

Formula Used:

Length of $\stackrel{⌢}{\text{AB}}=\frac{\theta }{360}\times 2\pi r$

Calculation :

Length of $\stackrel{⌢}{\text{AB}}=\frac{120}{360}\times 2\pi \times (6\sqrt{3})=4\pi \sqrt{3}$

b)

To determine

To find :The Length of arc.

Answer to Problem 9PSB

  $6\pi$

Explanation of Solution

Given Information :

  

The radius of $\stackrel{⌢}{\text{AB}}=\frac{\theta }{360}\times 2\pi r$

Formula Used:

Length of $\stackrel{⌢}{\text{AB}}=\frac{\theta }{360}\times 2\pi r$

Calculation :

Length of $\stackrel{⌢}{\text{AB}}=\frac{60}{360}\times 2\pi \times (18)=6\pi$

c)

To determine

To find : The Length of arc.

Answer to Problem 9PSB

  $9\pi$

Explanation of Solution

Given Information :

  

Radius of $\stackrel{⌢}{\text{AB}}(r)=\text{OA}=9$ units

Formula Used:

Length of are $=\frac{\theta }{360}\times 2\pi r$

Calculation :

Length of $\stackrel{⌢}{\text{AB}}=\frac{180}{360}\times (2\pi (9))=9\pi$