Question

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?

Answer 1

Doubling the sides of a cubical cell from 2-cm to 4-cm results in the surface area-to-volume ratio decreasing from 3 to 1.5, which demonstrates that as the size of the cube increases, its surface area-to-volume ratio decreases.

Step-by-step explanation:

When a cubical cell with 2-cm sides doubles the dimensions of its sides, the surface area-to-volume ratio decreases. For the original cube with a side of 2 cm, the surface area is 6×(2 cm)² = 24 cm² and the volume is (2 cm)³ = 8 cm³, which gives a surface area-to-volume ratio of 24 cm²/8 cm³ = 3.

If we double the sides to 4 cm, the surface area becomes 6×(4 cm)² = 96 cm² and the volume becomes (4 cm)³ = 64 cm³, resulting in a new surface area-to-volume ratio of 96 cm²/64 cm³ = 1.5. Therefore, the ratio of surface area to volume changes from 3 to 1.5, which is a decrease in the ratio as the size of the cube increases.

Answer 2

The ratio will become half.

Step-by-step 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