Question

Please show your working out/step by step explanation.

Answer 1

Answer:

r = 10/√3 ≈ 5.7735 cm

Step-by-step explanation:

Each coloured region is the same area, and we have 3 areas.

So, the area of purple circle represents (1/3) of the total area.

∴The radius of purple circle is r, and the radius of outer circle is 10 cm.

The area of the purple circle = π r²

The total area = area of outer circle = π * 10²

$\pi r^2 = \frac{1}{3} *\pi * 10^2 \\r^2 = \frac{1}{3} * 10^2\\r=\frac{1}{\sqrt{3} } *10=\frac{10}{\sqrt{3} } =5.774 \ cm$

So, the radius of the purple circle (r) = 5.7735 cm