They both increase with increasing cell radius (if we model a cell as a sphere). However, the rate of increase of the surface area is in general slower (dA/dr = 8πr) compared to the rate of increase of the volume (dV/dr = 4πr2). This would mean that with increasing cell size, the surface area to volume ratio is becoming smaller and smaller, giving a cell less surface area for the transport of nutrients for a given unit volume.
The Volume increases faster than the Surface Area
Not necessarily just changing the surface area causes the rate to change. Changing the ratio of surface area volume changes the rate at which a solute dissolves in a solvent. If the surface area is larger and the volume of a solute is smaller or the same, then the rate at which the solute dissolves in a solvent increases. If the surface area is smaller and the volume of the solute is larger or the same, then the rate at which the solute dissolves in a solvent decreases.
Area is proportional to a linear dimension squared, whereas volume is proportional to the linear dimension cubed. Thus, as a cell (or any object) increases in size, its volume grows proportionately more than its surface area.
The liquid will expand, it's volume will increase. If it becomes heated enough, it will evaporate (turn into a gas). The more heated it becomes, the more its volume must increase to keep the same pressure.
The rate of diffusion is affected by properties of a cell, the diffusing molecule, and the surrounding solution.
The Volume increases faster than the Surface Area
They grow
As a cell becomes larger the surface area to volume ratio gets smaller. The volume increases by the square of the surface area. That is the main reason that one celled organisms are small.
The surface area to volume ratio will increase
For a cube with edge length, L. Surface area = 6L2. Volume = L3. So ratio of Surface Area / Volume = 6 / L. Therefore, as the side length, L, increases, the ratio will decrease.
As the cell grows larger the ratio of surface area to volume increases. Larger cell = more volume for the amount surface area.
The volume of a body and the surface area arerelated but not in a direct way. For a given volume, the smallest surface area of an object is seen then the object is a sphere. As the shape flattens from a sphere, so the surface area becomes larger. When the object approaches an infinitely small thickness, the surface area approaches and infinite size.
Think o the volume of a box. As the base gets larger in perimeter, the surface area of the box becomes greater, and the volume increases.
They both increase with increasing cell radius (if we model a cell as a sphere). However, the rate of increase of the surface area is in general slower (dA/dr = 8πr) compared to the rate of increase of the volume (dV/dr = 4πr2). This would mean that with increasing cell size, the surface area to volume ratio is becoming smaller and smaller, giving a cell less surface area for the transport of nutrients for a given unit volume.
really.. the answer is that the volume also gets larger
I will rephrase your question: What happens to the surface area of a cube when the volume doubles. Ans. Surface area becomes 1.5876 times larger. Explanation: Let L = the length of the side of the original cube and h x L the length of the cube that is double the volume. Now: Vol= L^3 x 2 = (h x L)^3 or h = 2^(1/3) = 1.2599, so the length will be 1.2599 times larger. Surface area = 6 x L^2 for original cube and 6 x L^2 x 1.2599^2 for the cube with twice the volume. 1.2599^2 = 1.5876 If you are asking what happens to the surface area when the sides double, then the larger cube has surface area = 6 * 2^2 * L^2 , so 6 * 2^2 = 24. Each side is 4 times larger so the total surface area is 24 times larger.
Cell have a greater surface area to volume rations than a larger cell.