Question

three cubes of a metal whose edges are in the ratio 3: 4: 5 are melted and converted into a single cube diagonal of 12√3 cm. find edge of three cubes​

Answer 1

Step-by-step explanation:

Let the edges of three cubes be 3x, 4x and 5x cm respectively.

$Total \: volume \: of \: three \: cubes \\ = {(3x)}^{3} + {(4x)}^{3} + {(5x)}^{3} \\ = 27{x}^{3} + 64 {x}^{3} + 125{x}^{3} \\ = 216 {x}^{3} \\ Let\: a \:be\: edge \: of \:the\: cube \:so\: \\ formed\: \\ \therefore \: {a}^{3} = 216 {x}^{3} \\ a = 6x \\ Diagonal \:of \:new \:cube = 12 \sqrt{3} \:cm. \\ a \sqrt{3} = 12 \sqrt{3} \\ a = 12 \\ \implies \: 12 = 6x \\ x = \frac{12}{6} \\ x = 2 \\ 3x = 3 \times 2 = 6 \: cm \\ 4x = 4 \times 2 = 8 \: cm \\ 5x = 5 \times 2 = 10 \: cm$

Thus the edges of the three cubes are 6 cm, 8 cm and 10 cm respectively.