Chapter 11.8, Problem 3ST2

(a)

To determine

To Find: The length of $\stackrel{⌢}{AB}$ .

Answer to Problem 3ST2

  $\stackrel{⌢}{AB}=6\pi$

Explanation of Solution

Given: Radius is $12$ and $m\stackrel{⌢}{AB}=90$

Using arc length formula.

  $\begin{array}{l}\stackrel{⌢}{AB}=\frac{x}{360}\times 2\pi r\\ \stackrel{⌢}{AB}=\frac{90}{360}\times 2\pi (12)\\ \stackrel{⌢}{AB}=\frac{1}{4}\times 24\pi \\ \stackrel{⌢}{AB}=6\pi \end{array}$

(b)

To determine

To Find: The area of $AOB$ .

Answer to Problem 3ST2

  $36\pi$

Explanation of Solution

Given: Radius is $12$ and $m\stackrel{⌢}{AB}=90$

Using Area of sector formula.

  $\begin{array}{l}A=\frac{x}{360}\times \pi r^2\\ $ A=\frac{90}{360}\times \pi {(12)}^2$A=\frac{1}{4}\times 144\pi \\ A=36\pi \end{array}$

(c)

To determine

To Find: The area of region bounded by $\overline{AB}and\stackrel{⌢}{AB}$ .

Answer to Problem 3ST2

  $A=36\pi -72sq.units$

Explanation of Solution

Given: Radius is $12$ and $m\stackrel{⌢}{AB}=90$

Area of triangle

  $\begin{array}{l}{A}_t=\frac{1}{2}bh\\ A_t=\frac{1}{2}(12)(12)=72\end{array}$

Area of sector is $36\pi$

Therefore

Area of region is

  $A=36\pi -72sq.units$