Question

A cube of metal, each edge of which measures five cm, weighs $0.625kg$. What is the length of each edge of a cube of the same metal which weighs $40kg$?

Answer 1

Ratio of the weights of two cubes
$=0.625:40$
$=625:40\times 1000$
$=1:64$
Now ratio of the volumes of the two cubes
$1:64$
$\therefore$ Ratio of the edges of the two cubes
$=1:4$
(taking cube roots)
This means, the edge of the second cube is $4$ times the edge of the first cube, but the edge of the first cube is $5cm$
$\therefore$ the edge of the second cube $=4\times 5=20cm$