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The space diagonal of a cube measures 8√3 cm. What is the volume of the cube?

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NTPC CBT-I (Held On: 7 Jan 2021 Shift 2)
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  1. 512 cm3
  2. 512√3 cm3
  3. 1536√3 cm3
  4. 1536 cm3

Answer (Detailed Solution Below)

Option 1 : 512 cm3
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Detailed Solution

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Given:

The space diagonal of a cube = 8√3 cm

Formula used:

Diagonal of cube = √3a

Volume of cube = a3

Calculation:

According to the question

⇒ √3a = 8√3 cm

⇒ a = 8 cm

Now,

Volume of the cube = (8)3

⇒ 8 × 8 × 8 = 512 cm3

∴ The volume of the cube is 512 cm3

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