Answer:
The estimated amount of metal in the can is 87.96 cubic cm
Step-by-step explanation:
We can find the differential of volume from the volume of a cylinder equation given by
Thus that way we will find the amount of metal that makes up the can.
Finding the differential.
A small change in volume is given by:
So finding the partial derivatives we get
Evaluating the differential at the given information.
The height of the can is h = 26 cm, the diameter is 10 cm, which means the radius is half of it, that is r = 5 cm.
On the other hand the thickness of the side is 0.05 cm that represents dr = 0.05 cm, and the thickness on both top and bottom is 0.3 cm, thus dh = 0.3 cm +0.3 cm which give us 0.6 cm.
Replacing all those values on the differential we get
That give us
Or in decimal value
Thus the volume of metal in the can is 87.96 cubic cm.