How can volume be greater than surface area?

Answer 1

Let us begin with first saying that Volume will almost ALWAYS be greater than surface area considering it is in units cubed (to the third power, e.g. x^3) and surface area is units squared (to the second power, e.g. x^2)

However, I don't think this is the question. Yes volume can be greater than surface area. Example:

There is a cube with the dimensions 7x7x7

(V=hlw)The volume of this cube is going to be 7^3, or 7x7x7 = 343

(Sa=6lw)The surface area would be 6(7x7) or 6x7x7 = 294

A perfect example of when the NUMBER representing surface area is smaller than volume. Hope this helped! I'm actually on this subject right now in Eighth, so there's my bibliography, the good old noggin'.

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You cannot discreetly compare volume and surface area and claim that one is bigger. You could do it numerically, and the volume of a solid can numerically be greater, equal, or less than the surface area depending on what units you use. Consider a cube with side length 1 meter.

V = 1 m3, SA = 6 m2 <-- here, the surface area is numerically larger

Now suppose we say the side length of the cube is 100 centimeters:

V = (100 cm)3 = 106 cm3, SA = 6*(100 cm)2 = 6*104 cm2 <-- here, volume is numerically larger.

In both cases, we had a cube with the same dimensions but different units. This shows why we cannot easily say that the volume of a solid is greater or less than the surface area since they have different units (unit2 vs. unit3) and we can use a different unit (m vs. cm) and produce entirely different results.