The-area-of-a-circle-is-diretly-proportional-to-the-square-of-its-diameter-What-is-the-constant-of-proportionality-

Question Number 5556 by Rasheed Soomro last updated on 20/May/16

The area of a circle is diretly

proportional to the square of

its diameter .

What is the constant of proportionality ?

Commented by Yozzii last updated on 20/May/16

A \propto d^{2}

A = k {(2 r)}^{2} (d = 2 r > 0)

π r^{2} = 4 {k r}^{2}

\Rightarrow k = \frac{π}{4} .

A l t e r n a t i v e l y, s i n c e A = \frac{π}{4} d^{2}

\Rightarrow A \propto d^{2} \Rightarrow k = π / 4

Commented by Rasheed Soomro last updated on 20/May/16

Your way is better than the way

I saw in a book!