Chapter 0.2, Problem 1E

(a)

To determine

To find: The area of the circle as a function of its diameter $d$ .

Answer to Problem 1E

The area of the circle as a function of its diameter $d$ is equal to $\frac{\pi d^2}{4}$ .

Explanation of Solution

Given information:

The diameter of the circle is $d$ .

Calculation:

The area of the circle is given by

  $A=\pi r^2$ , where $r$ is a radius of the circle.

Since the diameter of the circle is $d$ , so the area of the circle is below:

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

Therefore, the area of the circle as a function of its diameter $d$ is $\frac{\pi d^2}{4}$ .

(b)

To determine

To find: The area of the circle.

Answer to Problem 1E

The area of the circle is equal to $4\pi$ square inches.

Explanation of Solution

Given information:

The diameter of the circle is $4$ inches.

Calculation:

From the part (a),

The area of the circle is $A=\frac{\pi d^2}{4}$ , where $r$ is a radius of the circle.

Since the diameter of the circle is $4$ inches, so the area of the circle is below:

  $\begin{array}{c}A=\frac{\pi {\left(4\right)}^2}{4}\\ =\frac{\pi \left(16\right)}{4}\\ =4\pi \end{array}$

Therefore, the area of the circle is $4\pi$ square inches.