Question

A cube of metal, each edge of which measures
5/8th of 9 cm weight of each edge of a cube of

the same metal which weighs 40 grams?​

Answer 1

your Question is -> A cube of metal, each edge of measures 5/8 th of 9 cm weights 625 grams. what is the length of each edge of a cube of the same metal weights 40 grams?

solution : let density of the metal is ρ.

volume of the cube of mass 625g, V = (5/8 × 9cm)³

= (45/8)³ cm³

so, density of metal cube, ρ = mass/volume

= 625/(45/8)³ g/cm³ ......(1)

let edge length of the cube of mass 40g = l cm

so, volume of the cube , v = l³ cm³

density of metal cube, ρ = mass/volume

= 40/l³ g/cm³ ......(2)

from equations (1) and (2) we get,

625/(45/8)³ = 40/l³

⇒125/(45/8)³ = 8/l³

⇒(5)³/(45/8)³ = (2)³/l³

⇒5/(45/8) = 2/l

⇒8/9 = 2/l

⇒l = 9/4 cm

Therefore the edge length of the cube is 9/4 cm or 2.25 cm.