Chapter 11.3, Problem 24PPS

To determine

To find: How much of each color of fabric will be needed to make multi-colored fabric clock.

Answer to Problem 24PPS

The required fabric of each color is $28.28$ in².

Explanation of Solution

Given information: Diameter of the clock is $12$ in. and all the four sectors in the clock are congruent.

Formula used: Area of sector $=\frac{\theta }{360}\times \pi r^2$

  $\theta =$ Angle of the shaded sector,

  $r=$ Radius of the circle.

Calculation: All the four sectors are congruent,

So, the angle of each sector $\theta =\frac{{360}^{\circ }}{4}={90}^{\circ }$

Here, $r=\frac{12}{2}=6$ , $\theta ={90}^{\circ }$ and $\pi =\frac{22}{7}$

Area of each sector,

A $=\frac{90}{360}\times \frac{22}{7}\times {\left(6\right)}^2$

A $=\frac{90}{360}\times \frac{22}{7}\times 36$

A $=28.28$ in²

Hence, the required fabric of each color is $28.28$ in².