So, the required percentage is [tex]5.81\%[/tex].
To understand the calculations, check below.
Area of the disk:
The area of the disk is defined as the ‘ measure of surface ‘ surrounded by the round edge (circumference) of the disk. The area of a disk can be derived by breaking it into a number of identical parts of disk as units — calculating their areas and summing them up till the disk is reformed.
That is [tex]Area=\pi \frac{d^2}{4}[/tex]
Let the width and the length of the flag be [tex]2x[/tex] and [tex]3x[/tex] respectively.
So, the diameter of the gold-colored disk will be [tex]\frac{2x}{3}[/tex]
Now, by using the above formula the area of the gold disk will be,
[tex]\pi \frac{d^2}{4}=\pi\times\frac{4x^2}{4\times 9} \\ =\frac{\pi x^2}{9}[/tex]
And the area of the flag will be,
[tex]Area=l\times b\\=2x\times 3x\\=6x ^2[/tex]
So, the required percentage is,
[tex]\frac{(\frac{\pi x^2}{9} )}{6x^2} \times 100=\frac{\pi}{54}\times 100\\ =5.81\%[/tex]
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