Chapter 11.3, Problem 3ACYP

To determine

To find: the area of the given shaded sector and round to the nearest tenth.

Answer to Problem 3ACYP

Area of the shaded sector $A=7.4f{t}^2$ .

Explanation of Solution

Given information: The given shaded sector is shown in below figure.

  

Formula used:

The area of a sector of the circle of radius r is:

  A = $\frac{x}{360}\pi r^2.$

Calculation:

The area of a sector of the circle of radius r is:

  $\begin{array}{l}A=\frac{x}{360}\pi r^2.\\ \text{From}\text{the}\text{given}\text{figure}\text{.}\\ x={53}^{\circ },r=4ft,\pi =\mathrm{3.14.}\\ A=\frac{53}{360}\times 3.14\times 4^2\\ A=7.4f{t}^2.\end{array}$