Answer:
The rate of the volume increase will be [tex]\frac{dV}{dt}=50.27 cm^{3}/s[/tex]
Step-by-step explanation:
Let's take the derivative with respect to time on each side of the volume equation.
[tex]\frac{dV}{dt}=4\pi R^{2}\frac{dR}{dt}[/tex]
Now, we just need to put all the values on the rate equation.
We know that:
dR/dt is 0.04 cm/s
And we need to know what is dV/dt when R = 10 cm.
Therefore using the equation of the volume rate:
[tex]\frac{dV}{dt}=4\pi 10^{2}0.04[/tex]
[tex]\frac{dV}{dt}=50.27 cm^{3}/s[/tex]
I hope it helps you!
