Question

Three cubes of a metal whose edge are in the ratio 3:4:5 are melted and converted
into a single cube whose diagonal is 12√3 cm. Find the edge of three cubes ​

Answer 1

Step-by-step explanation:

please mark my answer as brainest answer

Answer 2

ANSWER:

• Edge of three cubes is 6cm , 8cm ,10cm

GIVEN:

• Edges of three cubes are in the ratio 3:4:5
• When the three cubes are melted then a new cube of diagonal 12√3 is formed.

TO FIND:

• Edge of the three cubes.

SOLUTION:

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

Formula:

• Volume of cube = (Edge)³

Sum of the volume of three cubes = Volume of new cube.

=> (3x)³+(4x)³+(5x)³ = (Edge of new cube)³

=> 27x³+64x³+125x³ = (Edge of new cube)³

=> 216x³ = (Edge of new cube)³

=> Edge of new cube = 6x

Formula:

• Diagonal of cube = √3(Edge)

=> √3(6x) = 12√3

=> x = 2

Edge of three cubes:

= 3x

= 3(2)

= 6 cm

= 4x

= 4(2)

= 8cm

= 5x

= 5(2)

= 10cm