Question

three cubes of a metal whose edges are in the ratio 3 ratio 4 ratio 5 are melted and converted into a single cube whose diagonal is 12 root 3 cm find the age of 3 cubes

Answer 1

Plz mark it as brainlist,

See following solution image.....

Answer 2

$\textbf{Answer : } \\ \\ Let \: the \: ratio \: be \: x \\ \\  V_{1} = {(3x)}^{3} \\ \\ V_{2} = {(4x)}^{3} \\ \\ V_{3} = {(5x)}^{3} \\ \\ New \: formed \: Cube \\ \\ Diagonal \: of \: a \: Cube = Side \times \sqrt{3} \\ \\ Side = \frac {12 \sqrt{3}}{ \sqrt{3}} = 12cm \\ \\ V_{4} = {(12)}^{3} = 1728 \\ \\ \\ \textbf{A.T.Q} \\ \\ V_{4} = V_{1} + V_{2} + V_{3} \\ \\ 1728 = {(3x)}^{3} + {(4x)}^{3} + {(5x)}^{3} \\ \\ 1728 = 27{x}^{3} + 64{x}^{3} + 125{x}^{3} \\ \\ 1728 = 216{x}^{3} \\ \\ {x} = \frac {12}{6} = 2 \\ \\ Edge \: of \: first \: cube = 3x = 3 \times 2 = \bold{6cm} \\ \\ Edge \: of \: second \: cube = 4x = \bold{8cm} \\ \\ Edge \: of \: third \: cube = 5x = \bold{10cm}$