Chapter 7.8, Problem 55PPS

(a)

To determine

To find: The expression for the area of the larger circle.

Answer to Problem 55PPS

The area of the larger circle defined by the expression is $\pi r^2+18\pi r+81\pi$ .

Explanation of Solution

Given information:

The given table is

  

Calculation:

Calculate the area the larger circle.

  $\begin{array}{c}A=\pi {\left(r+9\right)}^2\\ =\pi \left(r^2+2\left(r\right)\left(9\right)+9^2\right)\\ =\pi \left(r^2+18r+81\right)\\ =\pi r^2+18\pi r+81\pi \end{array}$

Therefore, The area of the larger circle defined by the expression is $\pi r^2+18\pi r+81\pi$ .

(b)

To determine

To find: The expression of the area of the portion of the square outside the larger circle.

Answer to Problem 55PPS

The area of the square outside the larger circle is $1189.67-3.14r^2-56.52r$ .

Explanation of Solution

Given information:

The given table is

  

Calculation:

Calculate the area of the square.

  $\begin{array}{c}A=s^2\\ ={38}^2\\ =1444\end{array}$

Then the area of the square outside the larger circle,

  $\begin{array}{c}A=1444-\left(\pi r^2+18\pi r+81\pi \right)\\ =1444-\left(3.14r^2+56.52r+254.34\right)\\ =1189.67-3.14r^2-56.52r\end{array}$

Therefore, area of the square outside the larger circle is $1189.67-3.14r^2-56.52r$ .