What the radius of a circle with area 9?

Question

25724 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-15T01:48:05

Read below.

Happy $π$ $pi$ day!

Remember that:

$A = π r^{2}$ $A=pir^2$ The area of a circle is $π$ $pi$ times its radius squared.

We have:

$9 = π r^{2}$ $9=pir^2$ Divide both sides by $π$ $pi$ .

$\Rightarrow \frac{9}{π} = r^{2}$ $=>9/pi=r^2$ Apply square root on both sides.

$\Rightarrow \pm \sqrt{\frac{9}{π}} = r$ $=>+-sqrt(9/pi)=r$ Only the positive one makes sense(There can be only positive distances)

$\Rightarrow \sqrt{\frac{9}{π}} = r$ $=>sqrt(9/pi)=r$ Simplify the radical.

$\Rightarrow \frac{3}{\sqrt{π}} = r$ $=>3/sqrtpi=r$

$\Rightarrow \frac{3}{\sqrt{π}} \cdot \frac{\sqrt{π}}{\sqrt{π}} = r \cdot 1$ $=>3/sqrtpi*sqrt(pi)/sqrtpi=r*1$

$\Rightarrow \frac{3 \sqrt{π}}{π} = r$ $=>(3sqrtpi)/pi=r$

Just note that this is only a theoretical result.

Answer 2 · 2018-03-15T01:48:51

#sqrt(9/pi)

formula for finding area of a circle is given by,

       A =# pi r^2

This implies that,
9 = #pi r^2

r^2 = 9/pi

r = #sqrt(9/pi)