Chapter 1.2, Problem 68STP

To determine

To write: an expression to represent the area of the given circle.

Answer to Problem 68STP

  $A=\frac{\pi }{4}{\left(x+3\right)}^2$

Explanation of Solution

Given information:

A circle is given as shown:

  

Area of a circle is

  $A=\pi {\left(\frac{d}{2}\right)}^2$

Where d is diameter

Calculation:

Consider the given circle.

  

Here, diameter is $x+3$ .

So, expression for area of the circle can be evaluated as

  $\begin{array}{c}A=\pi {\left(\frac{d}{2}\right)}^2\\ =\pi {\left(\frac{x+3}{2}\right)}^2\\ =\frac{\pi }{4}{\left(x+3\right)}^2\end{array}$

Hence, the expression for areais $\frac{\pi }{4}{\left(x+3\right)}^2$ .