Question

Each layer of the structure below is a square. The base is made up of 100 cubes, the second layer 81 cubes and the third layer 64 cubes. If the top layer of the structure consists of 16 cubes, how many layers does the structure have in all?

Answer 1

Base has $100$ cubs = ${10}^2$ cubs ; $2^{nd}$ layer has $9^2$ cubs 6 so on

& to p has $16=4^2$ cubs $\therefore$ no of layers are :-

${\underset{–}{10}}^2,{\underset{–}{9}}^2,{\underset{–}{8}}^2,{\underset{–}{7}}^2,{\underset{–}{6}}^2,{\underset{–}{5}}^2,{\underset{–}{4}}^2=7layers$