Question

Three cubes of metal whose edges are in the ratio 3 : 4 : 5 are melted down into a single cube, whose diagonal is 12/3 cm. Find the edges of the three cubes.​

Answer 1

Answer:

edges are 6,8,10

Step-by-step explanation:

let sides be 3x, 4x,5x

then volume of new cube=(3^3+4^3+5^3)x^3

=216x^3

=6x^3

side of new cube =6x

diagonal=6x√3

then 6x√3=12√3

where x=2

hence edges are 6,8,10

Answer 2

Given:

☛ Ratio of edges of three cubes of metal 3 : 4 : 5

☛ Diagonal of the resultant cube is 12√3 cm.

To Find:

☛ edges of the three cubes

Solution:

☛ Ratio = 3 : 4 : 5

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

Also,

Diagonal of resultant cube = 4 cm

☛ Diagonal of a cube = √3 × edge

➜ 12√3 = √3 × edge

Cancel √3 both sides

➜ edge = 12 cm ------(i)

According to the question:

Three melted to form a single cube having diagonal 12√3 cm

So,

☛ Volume of three cubes = Volume of resultant cube

➜ (3x)³ + (4x)³ + (5x)³ = 12³ { from (i) }

➜ 27x³ + 64x³ + 125x³ = 1728

➜ 216x³ = 1728

➜ x³ = 1728 ÷ 216

➜ x³ = 8

➜ x = 2

Edges of the three cubes are 3x , 4x and 5x.

☛ Edge of cube 1 = 3x = 3×2 = 6 cm

☛ Edge of cube 2 = 4x = 4×2 = 8 cm

☛ Edge of cube 3 = 5x = 5×2 = 10 cm

Hence, edges are 6 cm, 8 cm and 10 cm.