Answer:
0.025 cm/min
Step-by-step explanation:
The volume rate of change is
[tex]\dfrac{dV}{dt} = 5[/tex]
We are to determine the rate of change of the radius. This is given by
[tex]\dfrac{dr}{dt}=\dfrac{dV}{dt}\div\dfrac{dV}{dr}[/tex]
The volume of a sphere is given by
[tex]V = \frac{4}{3}\pi r^3[/tex]
Hence,
[tex]\dfrac{dV}{dr} = 4\pi r^2[/tex]
Therefore,
[tex]\dfrac{dr}{dt}=\dfrac{5}{4\pi r^2}[/tex]
When r = 4,
[tex]\dfrac{dr}{dt}=\dfrac{5}{4\pi 4^2}=\dfrac{5}{64\pi}[/tex]
[tex]\dfrac{dr}{dt}=0.025 \text{ cm/min}[/tex]
Step-by-step explanation:
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