Chapter 9.8, Problem 11PSB

a.

To determine

To find:Thecoordinates of point E .

Answer to Problem 11PSB

The coordinates of point E are $\left(-3,0\right)$ .

Explanation of Solution

Given information:

Circle with center O .

Coordinates of point G are $\left(0,3\right)$ .

Formula used:

A circle with maintain same radius 3.

Calculation:

  

By inspection, point E is on x -axis. Its y coordinate will be 0.

Circle is of radius 3 and point E is on negative x axis. Its x coordinate will be -3.

The coordinates of point E are $\left(-3,0\right)$ .

b.

To determine

To find: The area of sector EPG .

Answer to Problem 11PSB

The area of sector EPG is $7.1$ .

Explanation of Solution

Given information:

Circle with center O .

Coordinates of point G are $\left(0,3\right)$ .

Formula used:

Area of a sector: $A_{EPG}=\frac{{90}^{\circ }}{{360}^{\circ }}(\pi {\left(r\right)}^2)$

Calculation:

  

  $\begin{array}{l}{A}_{EPG}=\frac{{90}^{\circ }}{{360}^{\circ }}(\pi {\left(r\right)}^2)\\ A_{EPG}=\frac{1}{4}(9\pi )\\ A_{EPG}\approx 7.1\end{array}$

c.

To determine

To calculate: The length of segmentGE .

Answer to Problem 11PSB

The length of segmentGE is $4.7$ .

Explanation of Solution

Given information:

Circle with center O .

Coordinates of point G are $\left(0,3\right)$ .

Formula used:

Length of a segment: $\stackrel{⌢}{GE}=\frac{{90}^{\circ }}{{360}^{\circ }}(\pi \left(2r\right))$

Calculation:

  

  $\begin{array}{l}\stackrel{⌢}{GE}=\frac{{90}^{\circ }}{{360}^{\circ }}(\pi \left(2r\right))\\ =\frac{{90}^{\circ }}{{360}^{\circ }}(\pi \left(2\ast 3\right))\\ =\frac{{90}^{\circ }}{{360}^{\circ }}(\pi \left(6\right))\\ \approx 4.7\end{array}$