Question

The area of a circle is given by A(r)=pie^2 and the radius in terms of the circumference is given by r(C)=C/2pie. Find A(r(C))

Answer 1

Answer:

$\large\boxed{A(r(C))=\dfrac{C^2}{4\pi}}$

Step-by-step explanation:

$A(r)=\pi r^2\\\\r(C)=\dfrac{C}{2\pi}\\\\A(r(C))\to\text{put}\ r=\dfrac{C}{2\pi}\ \text{to}\ A(r):\\\\A(r(C))=\pi\left(\dfrac{C}{2\pi}\right)^2\qquad\text{use}\ \left(\dfrac{a}{b}\right)^n=\dfrac{a^n}{b^n}\ \text{and}\ (ab)^n=a^nb^n\\\\A(r(C))=\pi\cdot\dfrac{C^2}{2^2\pi^2}\qquad\text{cancel one}\ \pi\\\\A(r(C))=\dfrac{C^2}{4\pi}$