If the Surface Area of a Cell Increases by a Factor

Question

If the surface area of a cell increases by a factor of 100,the volume of that cell will
A)remain the same.
B)increase by a factor of 100.
C)increase by a factor of 1000.
D)increase by a factor of 10.
E)decrease by a factor of 100.

Accepted Answer

The volume of a cell increases by the cube of the scale factor, so if the surface area (which increases by the square of the scale factor) increases by a factor of 100, the volume increases by the cube root of 100 squared, which is 1000.