Answer:
[tex]dV=542.9 cm^{3}[/tex]
Step-by-step explanation:
Let's start with the equation of the volume of a cylinder:
[tex]V=\pi r^{2}*h[/tex]
Where:
We can us partial derivatives to find the differential of this volume. So we will have:
[tex]dV=\frac{\partial V}{\partial r}dr+\frac{\partial V}{\partial h}dh[/tex] (1)
Now:
[tex]\frac{\partial V}{\partial r}=2\pi r*h=2\pi 12*60=4523.9 cm^{2}[/tex]
[tex]\frac{\partial V}{\partial h}=\pi 12^{2}=452.4 cm^{2}[/tex]
dr is a differential of the radius, so in our case it is 0.1 cm and dh, differential of the high, is 0.1*2 cm. We multiply by 2 because we need to consider the top and the bottom of the cylinder.
Now we just need to put all of this definitions in the equation (1).
[tex]dV=4523.9*0.1+452.4*0.2=542.9 cm^{3}[/tex]
I hope it helps you!
