What is the Volume of a Cube.

what is the Volume of a Cube if the number of a cubic units in its volume is twice the number of square units in its total surface area?
a 1827
b 1287
c 1872
d 1728

The balanced equation for this question is

X cubed or X^3 is twice the surface area or 6 (number of sides) times the surface area x^2 of one side.

That is... we use x as the length of one side. This is a variable or place holder that represents
the length of one side. As the question asks...

X^3 represents the volume

2*6*x^2 represents twice the surface area. * asterisk means times. Since the question states
that these are equal we get...

X^3 = 2*6*X^2 or

X^3 = 12*X^2

or... X*X*X = 12*X*X obviously X=12 or the lenght of a side of the cube equals 12

Since the question wants a volume for the cube. That is calculated by "cubing" or
multiplying the side length by itself 3 times...

12*12*12= 1728

so your answer would be D.

This story involves writing an equation for the two equal sides based on the simple length of
one side and illustrates the importance of knowing that both volume and surface area of a cube
can be calculated from knowing the length of a side.