Chapter 1.4, Problem 38PPE

To determine

To calculate: Area of the shaded part of the target.

Answer to Problem 38PPE

C. $A=60\pi$

Explanation of Solution

Given information: Radius of smallest circle is 2 inches. Distance between medium and smallest circle is 6 inches.

Formula used: Area of Circle is $\pi r^2$ where r is radius of circle.

Radius of smallest circle = 2inches.

Then, area of smallest circle =

  $\begin{array}{l}\pi 2^2\\ =4\pi \end{array}$

Radius of medium circle = (2+6) inches =8 inches.

Then, area of medium circle =

  $\begin{array}{l}\pi 8^2\\ =64\pi \end{array}$

Then, area of the shaded region= area of medium circle − area of smallest circle

  $\begin{array}{l}=64\pi -4\pi \\ =60\pi \end{array}$

Thus the correct equation is C. $A=60\pi$