Math Help - circle algebra

1. circle algebra {solved}

A new advertising symbol is to consist of three concentric
circles as shown, with the outer circle having a radius of 10 cm.
It is desired that the three coloured regions cover the same area.
Find the radius of the innermost circle in the figure shown.

how i tried to work it out: i did 10/3 to find the radius of the inner but answer says 10 root 3 / 3
above pic

2. area of the entire circle is $A = 100\pi \, cm^2$

let $r$ be the smallest inner radius

$\pi r^2 = \frac{100\pi}{3}$

solve

3. Originally Posted by skeeter
area of the entire circle is $A = 100\pi \, cm^2$

let $r$ be the smallest inner radius

$\pi r^2 = \frac{100\pi}{3}$

solve
Note that $\frac{1}{\sqrt(3)} = \frac{\sqrt3}{3}$ you get it by multiplying by $\frac{\sqrt(3)}{\sqrt(3)}$