A spherical cell takes in nutrients through its cell wall at a rate proportional to the area of the cell wall.The rate at which the cell uses nutrients is proportional to its volume.Which of the following expresses the rate at which the cell uses nutrients as a function of its radius, r.(A is a constant.)
A) $\frac{A}{r^{2}}$

B) $\frac{A}{r^{3}}$

C) $A r^{2}$

D) $A r^{3}$

Question

A spherical cell takes in nutrients through its cell wall at a rate proportional to the area of the cell wall.The rate at which the cell uses nutrients is proportional to its volume.Which of the following expresses the rate at which the cell uses nutrients as a function of its radius, r.(A is a constant.)
A) $\frac{A}{r^{2}}$

B) $\frac{A}{r^{3}}$

C) $A r^{2}$

D) $A r^{3}$

Quizplus · Accepted Answer

The rate at which the cell uses nutrients is proportional to its volume. The volume of a sphere is given by $\frac{4}{3}\pi r^{3}$. Since the rate is proportional to the volume, and the volume is proportional to $r^{3}$, the rate at which the cell uses nutrients as a function of its radius, $r$, is $A r^{3}$, where $A$ is a constant of proportionality.

A Spherical Cell Takes in Nutrients Through Its Cell Wall Ar2\frac{A}{r^{2}}r2A​

A Spherical Cell Takes in Nutrients Through Its Cell Wall $\frac{A}{r^{2}}$