Answer:
The area of the DVD is \(\\ 113.1cm^{2}\) (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 \(\\ A_{circle} = \pi * r^{2}\) [ 1 ].
We know that \(\\ d_{circle} = 2 * r\), 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 \(\\ \pi\) is a Greek symbol and is determined by dividing the circumference of a circle by its diameter:
\(\pi = 3.1415926535897932384626......\), although in practice \(\pi = 3.1416\).
To find what the DVD area is, and considering it as a circle, we can determine the area using [ 1 ].
We also know that \(\\ d_{circle} = 2 * r\), or:
\(\\ r = \frac{d_{circle} }{2} = \frac{12cm}{2} = 6cm\) .
So, the area of the DVD, with diameter of 12 centimeters is:
\(\\ A_{circle} = \pi * (6cm)^{2}\)
\(\\ A_{circle} = 36cm^{2} * \pi\) or
\(\\ A_{circle} = 113.0973355cm^{2}\) or rounded to the nearest hundredth:
\(\\ A_{circle} = 113.1cm^{2}\) (Because 0.097 = \(\\ \frac{97}{1000}\) ≈ \(\\ \frac{100}{1000} = \frac{1}{10} = 0.1\)).
So, the a DVD with diameter of 12 centimeters has an area of \(\\ 113.1cm^{2}\) (rounded to the nearest hundredth).
