three cubes of metal whose edges are in the ratio 3:4:5 are melted down into a single cube whose diagonal - Maths - Surface Area and Volume of a Cuboid and Cube

Question

three cubes of metal whose edges are in the ratio 3:4:5 are melted
down into a single cube whose diagonal is 12 root3cm find the edges
of three cube

Lovina Kansal · Accepted Answer

Solution :

Let s1, s2, s3 be the edges of the three cubes
Let s1 = 3x cm; s2 = 4x cm; s3 = 5x cmVolume of all three cubes = s13 + s23 + s33 = 3x3 + 4x3 + 5x3= 27x3 + 64x3 + 125x3=216x3 cm3Now, these three cubes are melted to form a single big cube
Let S be the length of each edge of the new cube formed
Now, volume of new cube = Volume of all three cubes ⇒S3 = 216x3⇒S = 6xLength of diagonal of new cube = 123 cm⇒3S = 123⇒S = 12 cmBut S = 6x⇒6x = 12 ⇒ x = 2 cmSo, s1 = 3×2 = 6 cm; s2 = 4×2 = 8 cm; s3 = 5×2 = 10 cm

three cubes of metal whose edges are in the ratio 3:4:5 are melted down into a single cube whose diagonal is 12 root3cm. find the edges of three cube.