SOLUTION: Consider a cube with edges of length s . In simplest terms, what is the ratio of the number of cubic inches in the volume of a cube to the number of square inches in its surface ar

Algebra ->  Surface-area -> SOLUTION: Consider a cube with edges of length s . In simplest terms, what is the ratio of the number of cubic inches in the volume of a cube to the number of square inches in its surface ar      Log On


   

Question 244890: Consider a cube with edges of length s . In simplest terms, what is the ratio of the number of cubic inches in the volume of a cube to the number of square inches in its surface area?
Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio is:

V/S = S/6

Consider a cube with sides of 3.

The volume (V) is 3*3*3

The Surface Area (S) is 6*3*3

The ratio of V/S = 3*3*3/6*3*3 = 3/6

The volume is 27 cubic inches.

The surface area is 54 square inches.

The ratio is 27/54 = 3/6 after you divide numerator and denominator by 9.

Now consider another cube with side of 14.

The volume is 14*14*14

The surface area is 6*14*14

The ratio of volume to surface area is:

14*14*14 / 6*14*14 = 14/6

The volume is 14^3 = 2744

The surface area is 6*14^2= 1176

The ratio of volume to surface area is 2744/1176 which is equivalent to 14/6 after you divide numerator and denominator by 196.

Your answer appears to be:

V/S = S/6