Chapter 11.3, Problem 5CYU

To determine

To calculate: The area of the shaded sector (minor) DCE with angle 57° of the given circle with radius 3 inches.

Answer to Problem 5CYU

The area of the shaded sector (minor) DCE is = 4.5 sq inches (nearest to tenth).

Explanation of Solution

Given information:

A circle with radius 3 inches and a minor sector DCE with angle 57°.

Calculation:

To calculate this shaded area, use the result

1. Area of the sector with radius r and angle θ is given by

  $\frac{\theta }{360}\times \pi r^2$

Now area of the minor sector DCE

= $\frac{\theta }{360}\times \pi r^2$

= $\frac{57}{360}\times \frac{22}{7}\times 3\times 3$

= $\frac{1254}{280}=4.478=4.5$ sq inches (nearest to tenth)