Surface area to volume ratio：練習問題

A cube-shaped organism has a side length of \(2\text{ cm}\). What is its surface area to volume ratio?

Why do small, single-celled organisms not require a specialized gas exchange system?

Which of the following is an adaptation in larger organisms to facilitate exchange as the surface area to volume ratio reduces?

Which of the following describes the relationship between the size of an organism and its surface area to volume ratio?

Explain why small, single-celled organisms do not require specialized gas exchange surfaces.

Compare the diffusion distance for oxygen in a small bacterium versus a large multicellular mammal.

Describe how the metabolic rate of an organism is typically related to its surface area to volume ratio.

Single-celled organisms can rely on simple diffusion for gas exchange, whereas large multicellular organisms require specialized exchange surfaces.
(a) Explain why a high surface area to volume ratio allows a single-celled organism to survive without a specialized gas exchange system.
(b) State one way in which the body shape of a large organism might be adapted to increase its surface area to volume ratio.

A spherical bacterial cell has a radius of \(1 \mu m\). A larger spherical protozoan cell has a radius of \(10 \mu m\).
The formula for the surface area of a sphere is \(4\pi r^2\) and the volume is \(\frac{4}{3}\pi r^3\).
(a) Calculate the surface area to volume ratio of the bacterial cell.
(b) Calculate the surface area to volume ratio of the protozoan cell.
(c) Use your answers to explain why the bacterial cell can exchange substances more efficiently than the protozoan cell.