If a cubical cell with 2-cm sides doubles the dimensions of its sides, what change occurs to the ratio of its surface area to volume?

The ratio will become half.

Explanation:

Given that the cell is cubic, its surface area = 6 l^2 where l is the length of sides in cm.

The volume is  l^3

The surface area of the cell is 2*2*6=24;

The volume of the cell is 8;

Surface Area : Volume = 24:8 = 3:1 ;

The new surface area is 4*4*6 = 96;

New Volume = 4*4*4=64;

Surface Area : Volume = 96:64 = 1.5:1