Express the surface area of a cube as a function of its volume v.

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Tanya Knox

Physics

12 December, 05:42

Express the surface area of a cube as a function of its volume v.

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Slade Leach · Answer 1

The surface area of a cube is:

S = 6l², making l the subject:

l = √ (S/6)

While the volume is:

V = l³

If we substitute l to get:

V = (√ (S/6)) ³

√ (S/6) = ³√V

S/6 = (³√V) ²

S = 6 (³√V) ² ⇒ 6V^ (2/3)