A set of nesting similar dolls

A set of hollow nesting dolls are similar solids. The largest doll has height \(20\) cm, surface area \(400\text{ cm}^2\) and volume \(1000\text{ cm}^3\). Each doll is similar to the one before it, with heights in the ratio \(4:5\) (smaller : larger).

1. Find the height, surface area and volume of the third doll.[3]
2. Show that the volume of the \(n\)th doll is \(1000(0.512)^{n-1}\text{ cm}^3\).[2]
3. Find the first doll in the set whose volume is less than \(100\text{ cm}^3\).[2]