A student builds a model of a high-rise for a diorama for an architecture class. The model is a perfect cube and the total volume is 500 cubic centimeters. How long is one side of the high-rise building? (Recall that the volume of a cube is calculated by l3, where l is the length of one side).

Volume of the cube (V) = 500cm^3

V = side/length (l) ^3 - - > so length of one side (l) = cube root (cr) of 500cm^3

This can be done on a calculator by using 500^ (1/3), since fractional exponents represent roots:

l = crV = cr500cm^3 = 7.937

= 7.94 cm

* you can verify this by cubing 7.94

--> 7.94^3 = ~500

The answer is 166.6666667