💬 👋 We’re always here. Join our Discord to connect with other students 24/7, any time, night or day.Join Here!

# (a) The volume of a growing spherical cell is $V = \frac {4}{3} \pi r^3,$ where the radius $r$ is measured in micrometers $(1 \mu m = 10^{-6} m).$ Find the average rate of change of $V$ with respect to $r$ when $r$ changes from (i) 5 to 8 $\mu m$ (ii) 5 to 6 $\mu m$ (iii) 5 to 5.1 $\mu m$(b) Find the instantaneous rate of change of $V$ with respect to $r$ when $r = 5 \mu m.$(c) Show that the rate of change of the volume of a sphere with respect to its radius is equal to its area. Explain geometrically why this result is true. Argue by analogy with Exercise 13(c).

## a) 540, 381,320 micrometer squaredb) 314 micrometer $^{3}$c) see solution

Derivatives

Differentiation

### Discussion

You must be signed in to discuss.

Lectures

Join Bootcamp

### Video Transcript

Oregon State University

Derivatives

Differentiation

Lectures

Join Bootcamp