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

Solution:

Given, three cubes of a metal has edges in the ratio 3:4:5

Three cubes are melted and converted into a single cube whose diagonal is 12√3 cm.

We have to find the edge of the three cubes.

Volume of cube = a³

Let the edge of the first cube = 3x

Volume = (3x)³ = 27x³

Let the edge of the second cube = 4x

Volume = (4x)³ = 64x³

Let the edge of the third cube = 5x

Volume = (5x)³ = 125x³

Volume of cubes after melting = 27x³ + 64x³ + 125x³

= 216x³ cm³

We know that the diagonal of the cube = side of the cube × √3

Let a be the side of the new cube.

Given, the diagonal of new cube = 12√3 cm

So, a√3 = 12√3

Side of new cube = 12 cm

Volume of new cube = 12³

Volume of three cubes after melting = volume of new cube

216x³ = 12³

x³ = 12³/216

x³ = (12/6)³

Taking cube root,

x = 12/6

x = 2

Now, the edge of the first cube = 3(2) = 6 cm

Edge of second cube = 4(2) = 8 cm

Edge of third cube = 5(2) = 10 cm

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

✦ Try This: Three cubes of a metal whose edges are in the ratio 2:3:4 are melted and converted into a single cube whose diagonal is 18√3 cm. Find the edges of the three cubes.

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 13

NCERT Exemplar Class 10 Maths Exercise 12.3 Sample Problem 5

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

Summary:

Three cubes of a metal whose edges are in the ratio 3:4:5 are melted and converted into a single cube whose diagonal is 12√3 cm. The edges of the three cubes are 6 cm, 8 cm and 10 cm

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