Answer:
The area of the DVD is [tex]\\ 113.1cm^{2}[/tex] (rounded to the nearest hundredth).
Step-by-step explanation:
The figure below is a circle of diameter 12 centimeter in the Cartesian coordinate system.
The area of a circle is [tex]\\ A_{circle} = \pi * r^{2}[/tex] [ 1 ].
We know that [tex]\\ d_{circle} = 2 * r[/tex], where d is the diameter (or the line segment that passes through the center of a circle and whose endpoints lie on it) and r is the radius of the circle (the distance from the circle's center to the circle's circumference).
Similarly, the circumference of a circle is the distance around a circle (the red line in the figure below).
The constant [tex]\\ \pi[/tex] is a Greek symbol and is determined by dividing the circumference of a circle by its diameter:
[tex]\pi = 3.1415926535897932384626......[/tex], although in practice [tex]\pi = 3.1416[/tex].
To find what the DVD area is, and considering it as a circle, we can determine the area using [ 1 ].
We also know that [tex]\\ d_{circle} = 2 * r[/tex], or:
[tex]\\ r = \frac{d_{circle} }{2} = \frac{12cm}{2} = 6cm[/tex] .
So, the area of the DVD, with diameter of 12 centimeters is:
[tex]\\ A_{circle} = \pi * (6cm)^{2}[/tex]
[tex]\\ A_{circle} = 36cm^{2} * \pi [/tex] or
[tex]\\ A_{circle} = 113.0973355cm^{2}[/tex] or rounded to the nearest hundredth:
[tex]\\ A_{circle} = 113.1cm^{2}[/tex] (Because 0.097 = [tex]\\ \frac{97}{1000}[/tex] ≈ [tex]\\ \frac{100}{1000} = \frac{1}{10} = 0.1[/tex]).
So, the a DVD with diameter of 12 centimeters has an area of [tex]\\ 113.1cm^{2}[/tex] (rounded to the nearest hundredth).
