Question

If l is the length of a diagonal of a cube of volume V, then
A. 3V=l³
B. V=l³
C. 3V=2 l³
D. 3V= l³

Answer 1

Concept used :  

Diagonal of a cube = √a² + a² + a² = √3a² = √3a

The line segment joining the opposite vertices is called a diagonal of a cube.

Mistake in the options :  

A. 3V = l³

B. √3V = l³

C. 3√3V = 2 l³

D. 3√3V = l³

Given: l is the length of a diagonal of a cube of volume V.

Diagonal of a cube ,l = √3a

Edge of a cube , a = l/√3

Volume of cube , V = a³

V = (l/√3)³

V = l³/(3√3)

l³ = 3√3V

Option (D)  l³ = 3√3V  is correct.

HOPE THIS ANSWER WILL HELP YOU…..

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Answer 2

Diagonal = √3a

Volume = a^3

Thus;

a = l/(√3)

a = ³√V

a = a

l/√3 = ³√V

Cubing on both sides:

l³ = 3√3 V

That's the solution.