Question

Let circumference of a circle is $S$ and area of the circle is $A$. Then which of the following is true.

• A. $S=4\pi r^{2}A$
• B. $\pi S=4A$
• C. $S^2=2\pi A$
• D. $S^2=4\pi A$

Answer 1

The correct option is D $S^2=4\pi A$

Let $r$ be the radius of the circle.

Then $S=2\pi r$ and $A=\pi r^2$.

Now, $S^2=4{\pi }^2{r}^2=4\pi \left(\pi r^2\right)=4\pi A$.