Q: How will surface area to volume ratios of a small cell compare to those of a large cell?

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Simply knowing the volume and surface area is not enough information to determine the shape. There is a table of SA/V ratios, but they become distorted for large and small values, so there is no way to tell.

The volume of the 6 cm sphere is 1.53 = 3.375 times as large.

The ratios are "small to large".

A smaller cell has a higher surface area to volume ratio. A reason for this is volume is cubic (3D) and surface area is 2D so when surface area increases a little bit, the volume increases exponentially. And when the surface area shrinks a little bit, the volume decreases exponentially.

If the surface area of the organism is small, then there is no problem with getting all the oxygen needed. If the surface area of the organism is large, therefore a special respiratory surface is needed. An example is lungs, gills. The ratio of surface area to volume in a small organism is greater than the ratio in a large organism.

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they have a greater surface-to-volume ratio

Having a large surface area to volume ratio allows root hairs to quickly absorb water and nutrients from the soil.

Simply knowing the volume and surface area is not enough information to determine the shape. There is a table of SA/V ratios, but they become distorted for large and small values, so there is no way to tell.

As a cell becomes larger, its volume increases faster than its surface area. This results in a decrease in the surface area to volume ratio. A high surface area to volume ratio is important for efficient exchange of nutrients and waste with the cell's environment.

A small amount of ice generally melts faster than a large amount of ice because of the difference in surface-area to volume ratios. Heat transfer with the surroundings occurs only at the boundaries of the ice. The rate of melting is thus directly proportional to the surface area. Additionally, the amount of ice to be melted is dependent on the volume. The more ice, the longer it takes to melt. Thus, a small cube of ice will melt faster because it has a greater surface area to volume ratio than a large block of ice.

The respiratory system has evolved to maximize surface area-to-volume ratios in structures like the alveoli in the lungs, allowing for efficient gas exchange with the bloodstream. The extensive network of capillaries surrounding the alveoli increases the available surface area for oxygen and carbon dioxide exchange, while minimizing the distance over which diffusion occurs. This adaptation enhances the efficiency of gas exchange by optimizing the diffusion of gases across cell membranes.

It will decrease. In a larger cell, you have less surface area per volume.

Small organisms, like a amoeba's, have large surface area : volume ratios which means the exchange can take place by diffusion through the cell wall, the same as any other single celled organsism.

A millimeter is not equivalent to any volume, no matter how large or small, because "millimeter" is not a unit of volume, so there's no way to compare it to any volume.

The volume of the 6 cm sphere is 1.53 = 3.375 times as large.

The ratios are "small to large".

A smaller cell has a higher surface area to volume ratio. A reason for this is volume is cubic (3D) and surface area is 2D so when surface area increases a little bit, the volume increases exponentially. And when the surface area shrinks a little bit, the volume decreases exponentially.