Question

Three metallic cubes whose edges are in the ratio 3:4:5 are melted to form a single cube whose diagonal is 12v3 cm. What are the lengths of the edges of the three cubes?

(a) 3 cm, 4 cm, 5 cm
(b) 6 cm, 8 cm, 10 cm
(c) 9 cm, 12 cm, 15 cm
(d) 1.5 cm, 2 cm, 2.5 cm 337​

Answer 1

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

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3 Now, let a be the edge of the new cube so formed after melting

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3 Now, let a be the edge of the new cube so formed after melting Then we have, a3 = 216x3 a = 6x

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3 Now, let a be the edge of the new cube so formed after melting Then we have, a3 = 216x3 a = 6x We know that, Diagonal of the cube

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3 Now, let a be the edge of the new cube so formed after melting Then we have, a3 = 216x3 a = 6x We know that, Diagonal of the cube = √(a2 + a2 + a2)

Let the edges of three cubes (in cm) be 3x, 4x and 5x respectively. So, the volume of the cube after melting will be = (3x)3 + (4x)3 + (5x)3 = 9x3 + 64x3 + 125x3 = 216x3 Now, let a be the edge of the new cube so formed after melting Then we have, a3 = 216x3 a = 6x We know that, Diagonal of the cube = √(a2 + a2 + a2) = a√3 So, 12√3 = a√3 a = 12 cm x = 12/6 = 2

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

Answer 2

Answer:

The edges of the 3 cubes are 6 cm, 8 cm, 10 cm

Step-by-step explanation:

Let the edges of the cube be 3x,4x and 5x

It is given that these cubes are melted to form a single cube whose diagonal is $12\sqrt{3}$ cm

The volume of new cube formed = 3³x³+4³x³+5³x³=216x³=(6x)³

Side of the new cube is 6x and its diagonal is 6x√3cm

Given that 6x√3=12√3

⇒6x=12

⇒x=2

Hence, The edges of the 3 cubes are 6 cm, 8 cm, 10 cm