Chapter 11.3, Problem 38PPS

To determine

The area of the shaded region.

Answer to Problem 38PPS

The area of the shaded region is 12.6 sq. units.

Explanation of Solution

Given: A circle with radius 4 units as shown below-

  

Concept Used: The formula for the area of the sector of a circle with central angle $\theta$ and radius r is given by-

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

Calculations: From the graph, the radius of the circle can be easily determined, which is 4 units.

The central angle of the shaded sector is $90°$ . Thus, area of the shaded region is-

Shaded area $=$ $\frac{90°}{360°}\times \pi {\left(4\right)}^2$ sq. units

  $=\frac{1}{4}\times 3.14\times 16$ sq. units

  $=12.6$ sq. units (approx.)

Thus, area of the shaded region is 12.6 sq. units (approx.).