Question

the cubes of three cubes of 15 cm,12cm and 9cm respectively are melted together to form into a single cube find the diagonals of the cube.​

Answer 1

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18$\large\mathrm{\sqrt{ 3 }}$

volume of cube = side into side into side

Using this formula,

Volume of cube of 15 cm = 3375cm cube

Volume of cube of 12cm = 1728cm cube

Volume of cube of 9cm = 729cm cube

Total volume of new cube = 3375 + 1728 + 729

= 5832 .

Side of new cube = $\large\mathrm{\sqrt{ 5832 }}$

= 18 cm.

diagonal of new cube = $\large\mathrm{\sqrt{ 3}}$ × side

= $\large\mathrm{\sqrt{ 3 }}$ × 18

= 18$\large\mathrm{\sqrt{ 3 }}$cm.