Question

3 cubee of metel whose edges are in the ratio 3:4:5 are method down into a single cube whose diagonal is 12root 3 cm find the edges

Answer 1

Given, the edges of 3 cubes, in the ratio 3:4:5, are melted down to form a large cube of diagonal 12√3 cm
Now, diagonal of a cube = a√3
∴ 12√3 = a√3 ⇒ a = 12cm
Hence, edge of the new cube = 12cm
Now, Sum of volume of three smaller cubes = Volume of large cube
Let the edges of the three cubes be 3x, 4x and 5x respectively.
∴ (3x)³ + (4x)³ + (5x)³ = (12)³
⇒27x³ + 64x³ + 125x³ = 1728
⇒216x³ = 1728
⇒x³ = 8
⇒x = 2
Hence the edges of the 3 cubes are 6cm, 8cm and 10cm respectively.