A cube has a volume of ##15625## ##cm^3##. What is the surface area in ##cm^2##?

##SA=3750cm^2##

The volume of a cube is determined by the formula ##V=s^3## where ##s## is the measurement of each edge.

Since cube has six square faces, each of the faces will have the area of a square which we know to be ##A=s^2##. Therefore the total surface area of a cube will be the area of a square multiplied by six (faces).

##SA=6s^2##

Solving for the length of edge (side):

##V=s^3##

##s=root(3)(V)=root(3)(15625cm^3)##

##s=25cm##

Solving for the surface area:

##SA=6s^2=6(25cm)^2##

##SA=3750cm^2##