Question

The volume of two cubes are in the ratio 8:27 then their sides will be in the ratio

Answer 1

volume of cube 1 = 8 = 2^3
volume of cube = ( side of cube ) ^3
side of cube 1 = cube root 8 = 2 cm

volume of cube 2 = 27 = 3^3
side of cube 2 = cube root 27 = 3 cm

therefore, 8:27 = 2:3

Answer 2

Volume of cube = (side)³
now assuming volume of both cube be
8V, 27V

as volumeA : volumeB = (sideA)³ : (sideB)³
So
=> 8V : 27V = (8V)⅓ : (27V)⅓
=> sideA : sideB = (8V)⅓ : (27V)⅓
so now using property of ratios
=> (8V)⅓ : (27V)⅓ = 2(V)⅓ : 3(V)⅓ = 2:3
=> sideA : sideB = 2 : 3
so ratio of side of cubes will be 2:3