How area becomes pie d square divided by four
Answers
Answer:
I assume you mean
A=πd24
where you divide the diameter (d) squared by 4.
There is a short and a long answer to this question. The short answer comes from the expression of the circle's surface area
A=πr2
where r is the radius of the circle. Since the diameter is twice the radius,
r=d2
when you square both sides, you get
r2=d222=d24
plug this back in the circle's area expression
A=πr2=πd24
The long answer comes from integration, where you integrate to reach the result
A=πr2
itself. The area of a circular annulus (a disk with a hole in it) of an infinitesimal thickness dr is given by
dA=2πrdr
The circle is nothing but a number of concentric annuli of radii ranging between 0 and R, the circle's radius, the total area of the circle is the sum of the areas of all the annuli, which you can sum up by integrating the above expression
A=∫R0dA=∫R02πrdr=πr2
Explanation: