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Which of the following statements about l, the length of a diagonal of a cube of volume V is true?

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3 V = l 3

3 V = l 3

33 V = 2 l 3

33 V = l 3

answer is D.

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Detailed Solution

Given that, l is the length of the diagonal of the cube of volume V.
We know that, volume of cube

= a 3

, where a is the side of the cube.
Length of diagonal of cuboid,

l = 3 a

.
We will first determine the value of side of a cube in terms of diagonal length-

⇒ 3 a = l

⇒ a = l 3

Now, we will equate the value with the volume-

⇒ V = a 3

⇒ V = (l 3) 3

⇒ 33 V = I 3

So, the relation between the volume V and the length of the diagonal is

33 V = l 3

.
Hence, option 4 is the correct option.

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