Question

A DVD has a diameter of 12 centimeters. What is the area of the DVD? Round your answer to the nearest hundredth.

Answer 1

12÷6=6
A=3.14×6^2
A= 113.04cm

Answer 2

The area of the DVD is
`\\ 113.1cm^(2)` (rounded to the nearest hundredth).

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 = (d_(circle) )/(2) = (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 =
`\\ (97)/(1000)` ≈
`\\ (100)/(1000) = (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).