Explain which cell in the figure above would be most efficie

Explain which cell in the figure above would be most efficient in removing internal cell waste by diffusion. (Note: the formula for the surface area of a cube is 6s², and the formula for the volume of a cube is s³, where s = the length of a side of the cube.) Support your answer with mathematical data.

Thanks! (AP Biology)

Solution

The smaleest cube (10um) will be the most efficient in removing internal cell waste by diffusion with respect to other cubes.

Reason : With increasing size of the cubes, it takes more time for the cell waste to diffuse through all the area and remove the internal cell waste. It will take longer for the waste to reach the cube centre although diffusion rate is same for all the cube. The surfacearea/volume ratio decreases with increase in the volume of the cube. Smaller ratio of surface area is present in the largest cube as compared to the smaller ones that has bigger surface area. This means that the cell waste can diffuse faster in the smallest cell cube as it has less surface area with respect to the bigger cube. Smaller cube surface area= 6s²= 6*(10)²⁼ 600um2 and Larger cube surface area= 6s²= 6*(30)²⁼ 1800um2.