# The diameter of a DVD is 12 centimeters. The hole in the center of a DVD has a diameter of 1.5 centimeters. Find the area of the DVD. Round to the nearest hundredth if necessary.

2 months ago

## Solution 1

Guest #3209
2 months ago

The area of the circular DVD is given by A = 111.33 cm²

### What is a Circle?

A circle is a closed figure in which the set of all the points in the plane is equidistant from a given point called “center”. Every line that passes through the circle forms the line of reflection symmetry. Also, the circle has rotational symmetry around the center for every angle

The circumference of circle = 2πr

The area of the circle = πr²

where r is the radius of the circle

The standard form of a circle is

( x - h )² + ( y - k )² = r²,

where r is the radius of the circle and (h,k) is the center of the circle.

The equation of circle is ( x - h )² + ( y - k )² = r²

For a unit circle , the radius r = 1

x² + y² = r² be equation (1)

Now , for a unit circle , the terminal side of angle θ is ( cos θ , sin θ )

Given data ,

Let the area of the circular DVD be A

Let the diameter of the DVD = 12 cm

So , the radius of the DVD = 6 cm

Now , the diameter of the hole = 1.5 cm

So , the radius of the hole = 0.75 cm

And , area of the circular DVD be A = π [ ( 6 )² - ( 0.75 )² ]

On simplifying , we get

The area of circular DVD is A = π ( 36 - 0.5625 )

The area of circular DVD is A = π ( 35.4375 )

The area of circular DVD is A = 111.33 cm²

Hence , the area of the circular DVD is 111.33 cm²

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## Solution 2

Guest #3210
2 months ago
111.27 centimeter squared.

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