Question

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).

Answer 1

The answer is 166.6666667

Answer 2

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