Question

Each side of a cube is decreased by 50%. Then what will be the ratio of volumes of the original cube and the decreased rube ?

Answer 1

Let the length of each side of the cube be a units.
` therefore` fhe volume of the cube `=a^3` cubic-Lmits
After decreasing the length of e,ach side by 50%, the length of each sides becomes `(a-a xx 50 / 100)` units `= a/2 ` units .
` therefore` the volumes of the decreased cube `=(a/2)^3` cubic -units `=(a^3)/(8)` cubic-units.
`therefore ` ( volumes of the original cube):( volume of the decreased cube)
`a^3 : (a^3)/(8) =1 : 1/8 = 8 : 1 `
Hence the required ratio = 8:1