Three cubes with sides in the ratio of 3 ∶ 4 ∶  5 are melted to form a single cube whose diagonal is 18√3 cm. The sides of the three cubes are:

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SSC CGL 2023 Tier-I Official Paper (Held On: 20 Jul 2023 Shift 1)
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  1. 21 cm, 28 cm and 35 cm
  2. 9 cm, 12 cm and 15 cm
  3. 18 cm, 24 cm and 30 cm
  4. 12 cm, 16 cm and 20 cm

Answer (Detailed Solution Below)

Option 2 : 9 cm, 12 cm and 15 cm
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Detailed Solution

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Given:

Three cubes with sides in the ratio of 3 ∶ 4 ∶  5 are melted to form a single cube whose diagonal is 18√3 cm.

Concept used:

The diagonal of a cube = √3a (where a is the sides)

Calculation: 

Let the s sides of the cubes will be 3x cm , 4x cm, and 5x cm

As per the question,

Volume of the new cube is 

(3x)3 +( 4x)3 +( 5x)3 = 216 x3.

⇒ side is = 6x

diagonal is 6x√3

⇒  6x√3 = 18√3

⇒ x = 3

The sides of the cubes will be 9 cm , 12 cm, and 15 cm

∴ The correct option is 2

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