Chapter 4.3, Problem 20PPE

To determine

Rule that represent area of the grass as a function r.

Answer to Problem 20PPE

  $A=\left(4-\pi \right)r^2$

Explanation of Solution

Given:

The given figure is,

  

The radius of circular fountain is r .

Side of square a = 2r

The area A of the grass is,

A = area of square − area of circle

  $\begin{array}{l}A={\left(2r\right)}^2-\pi r^2\\ =4r^2-\pi r^2\\ \Rightarrow A=\left(4-\pi \right)r^2\end{array}$

Therefore, the rule of area A of the grass as the function of r is

  $A=\left(4-\pi \right)r^2$