Question

In a circle, area and circumference can be found using the formulas A=(pi)r^2 and C=2(pi)r, respectively, Write a formula for A in terms of C.(your answer should not contain r)

Answer 1

`A = (C^2)/(4\pi)`

Explanation:

Given that

Area of a circle
`A=\pi r^2`

Circumference of the circle
`C = 2 \pi r`

Let us re-write the equation of area of circle:

`A=\pi r^2`

`A = \pi * r * r`

Multiplying and dividing with 2:

`A = (2\pi r)/(2) * r\\\text{Putting }2\pi r = C:\\\Rightarrow A = (C)/(2) * r\\\text{Multiplying and dividing by } 2\pi:\\\Rightarrow A = (C)/(2) * (2\pi r)/(2\pi)\\\text{Putting }2\pi r = C:\\\Rightarrow A = (C * C)/(4 \pi)\\\Rightarrow A = (C^2)/(4 \pi)`

Hence, A in terms of C can be represented as:

`A = (C^2)/(4\pi)`