Question

Suppose that the radius is expanding at a rate of 0.6 inches per second. How fast is the volume changing when the radius is 2.8 inches? Use at least 5 decimal places in your answer.

Answer 1

Answer:

59.11221 in^3/s

Step-by-step explanation:

Given dr/dt = 0.6 in/s

Find dV/dt when r = 2.8 in.

$V=\frac{4\pi r^3}{3}$

so $\frac{dV}{dr}=4\pi r^2$

$\frac{dV}{dt}=\frac{dV}{dr}\cdot\frac{dr}{dt}=4\pi r^2\cdot\frac{dr}{dt}$

Use r = 2.8 in and dr/dt = 0.6 in/s

get

$\frac{dV}{dt}=59.11221 in^3/s$