what is the derivation for the formula of the  area of a circle?i would like to know how it is derieved. pl help...

2 Answers

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

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The area of the circle is a function of radius of that circle.

A(r) = `pi` *r^2

We'll calculate the derivative of the area, differentiating with respect to r.

Since `pi` is a constant, we'll differentiate r^2, using the derivative formula:

(x^n)' = n*(x^(n-1))*(x)'

(x^n)' = n*(x^(n-1))*1

(x^n)' = n*(x^(n-1))

Comapring, we'll get:

(r^2)' = 2*(r^(2-1))*(r)'

(r^2)' = 2*r

dA/dr = A'(r) = 2`pi` r (circumference of the circle)

The requested derivative of the area of circle is dA/dr = A'(r) = 2`pi` r.