Chapter 11.3, Problem 3CCYP

To determine

To calculate: The area of the shaded sector (major) with angle 65° of the given circle with radius 11 inches.

Answer to Problem 3CCYP

The area of the shaded sector (major) is = 100.4 sq inches (nearest to tenth).

Explanation of Solution

Given information:

Circle with radius 11 inches and a minor sector JKL with angle 65°.

Calculation:

Required shaded sector (major sector) area=area of the circle − area of the minor sector JKL.

To calculate this shaded area, he will use two results

1. Area of the circle with radius r is given by

  $A=\pi r^2$

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

  $\frac{\theta }{360}\times \pi r^2$

So area of the given circle is

  $A=\pi r^2$

  $A=\frac{22}{7}\times 11\times 11$

= $\frac{2662}{7}squareinches$ ………….......(I)

Now area of the minor sector

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

= $\frac{65}{360}\times \frac{22}{7}\times 11\times 11$

= $\frac{17303}{252}$ sq inches….......(II)

Required shaded sector (major sector) area=area of the circle − area of the minor sector JKL.

= $\frac{2662}{7}squareinches$ - $\frac{17303}{252}$ sq inches

=100.353sq inches.

=100.4 sq inches (nearest to tenth)