Chapter 11.3, Problem 3DCYP

To determine

To calculate: Area covered by green hues means area of a sector of the given circle (color wheel) whose diameter is given 10 inches.

Answer to Problem 3DCYP

Area of the green hues sector of the given circle (color wheel) =6.5 sq inches (nearest to tenth).

Explanation of Solution

Given information:

Given12 congruent colored parts of the circle with diameter 10 inches.

Calculation:

So to calculate the area of the green hues sector, must know two things

1. Congruent geometry:- any two geometry are said to be congruent if they have same angles and same sides

Means both geometries look same to each other in every aspect.

2. Area of the given sector with radius r
A= $\frac{\theta }{360}\times \pi r^2$

Where r is the radius of the circle .

Now firstly find the angle that made by a sector which is congruent to other 11

Equal parts.

Hence $\theta =360/12=30$ °

  $\begin{array}{l}Henceradiusofthecircle=halfofthediameter=\frac{10}{2}=5inches\hfill \\ SoArea=\frac{30}{360}\times \frac{22}{7}\times 5\times 5\hfill \\ =\frac{1}{12}\times \frac{22}{7}\times 25\hfill \\ =\frac{550}{84}\hfill \\ =6.5476squareinches\hfill \end{array}$

=6.5 sq inches (nearest to tenth)