Surface area to volume ratio：練習題

A hypothetical organism is spherical with a radius of \( 0.5\text{ mm} \). If this organism grows such that its radius increases to \( 1.5\text{ mm} \), what is the factor by which its surface area to volume ratio (SA:V) has changed?

A scientist is studying four species of mammals with different body masses. Which species is likely to have the highest oxygen consumption per unit of body mass to maintain its body temperature?

Large organisms have evolved specialized exchange surfaces and mass transport systems. Which of the following is a mathematical consequence of increasing the size of an object that necessitates these systems?

A hypothetical cube-shaped cell has a surface area to volume ratio (SA:V) of \( 6.0\text{ mm}^{-1} \). If all the dimensions of the cell are doubled, what will be the new surface area to volume ratio?

Which of the following modifications to the body shape of a large multicellular organism would most effectively increase its surface area to volume ratio without significantly changing its total volume?

A student observes that the rate of simple diffusion of a lipid-soluble molecule decreases as the side length of a cubic organism increases. Explain this observation in terms of surface area to volume ratio.

A spherical cell has a radius of \( r \). If the radius of the cell increases by a factor of 3, explain the effect on the surface area to volume ratio and its impact on the rate of oxygen uptake.

A hypothetical cube-shaped cell has a side length of \( s \). If the side length is reduced to \( \frac{1}{3}s \), calculate the factor by which the surface area to volume ratio (SA:V) changes.

A student calculated the surface area to volume ratio of three different organisms: a unicellular amoeba, a flatworm, and a large mammal.

a) Calculate the surface area to volume ratio of a cube with a side length of \( 2 \text{ cm} \). Show your working. (2 points)
b) Explain why a large mammal requires a specialized mass transport system, such as a circulatory system, while a unicellular organism does not. (3 points)