Chapter 8.7, Problem 29E

To determine

To select: the correct option representing the area of the shaded portion for the given figure.

Answer to Problem 29E

  $\text{B}$

Explanation of Solution

Given information:

The figure is shown below.

  

The options are as follows:

  $\begin{array}{cc}\begin{array}{l}\text{A}\\ \text{B}\\ \text{C}\\ \text{D}\\ \text{E}\end{array}& \begin{array}{l}19\pi \\ 16\pi \\ 9\pi \\ 4\pi \\ 2\pi \end{array}\end{array}$

Calculation:

The radius of outer circle $\left(r_o\right)$ and inner circle $\left(r_i\right)$ is 5 units and 3 units respectively.

The area of shaded portion $\left(A\right)$ can be evaluated as follows:

  $\begin{array}{l}A=A_{outer}-A_{inner}\left[\text{Using area of circle}\right]\\ =\pi {\left(r_o\right)}^2-\pi {\left(r_i\right)}^2\left[\text{Put the value of }{r}_o\text{and }{r}_i\right]\\ =\pi {\left(5\right)}^2-\pi {\left(3\right)}^2\\ =25\pi -9\pi \\ =16\pi \end{array}$

Since the area of shaded portion is $16\pi$ , thus option B is correct.