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Q.

The volume of a cube with diagonal of length d units is $\frac{d^{3}}{3 \sqrt{3}}$ cu. units.

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a

True

b

False

c

Data insufficient

d

None of the above

answer is A.

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Detailed Solution

A cube's diagonal is the line that runs through its middle. The cube's face diagonal is not the actual diagonal. Find the relationship between the cube's diagonal and sides, then substitute the cube's side for the diagonal to determine the volume of the cube.
We know that the length of the diagonal of the cube of side a is

a \sqrt{3}

=d
So, a=

\frac{d}{\sqrt{3}}

Hence, the volume=

a^{3} = {(\frac{d}{\sqrt{3}})}^{3} = \frac{d^{3}}{3 \sqrt{3}}

Hence the statement is true.

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