Chapter 10.9, Problem 6PSA

a)

To determine

To find : Length of $\stackrel{⌢}{\text{AB}}$

Answer to Problem 6PSA

  $\text{9}\text{.42}$ units

Explanation of Solution

Given Information :

  

Radius of given circle = $\text{6}$

Formula Used:

Length of the arc = $\frac{\theta }{\text{360}}\times 2\pi r$

Calculation :

Length of the arc

  $\begin{array}{l}=\frac{90}{360}\times 2\times \pi \times 6\\ =3\pi \\ =9.42\text{ units}\end{array}$

b)

To determine

To find : Perimeter of the sector AOB.

Answer to Problem 6PSA

  $21.42$ units

Explanation of Solution

Given Information :

The given information is Radius of circle = $6$ units.

Formula Used:

Perimeter = $2r$ + Length of the arc

Calculation :

Perimeter of the sector AOB (Shaded region of sector)

  $\begin{array}{l}=2\times 6+\frac{90}{360}\times 2\times \pi \times 6\\ =12+9.42\\ =21.42\text{ units}\end{array}$