Suppose a soup can is made from a sheet of steel19 which is .13 mm thick. If the can is 11 cm high and 6 cm in diameter, use differentials to estimate the mass of the can. The density of the steel being used is 8000 kg/m3

The can mass is 0,00359 kg or 3,59 g

Explanation:

1. Relevant Data:

Steel thickness= 0.13 mm or 0.013 mm

h=11 cm

d=6 cm

ρ=800 kg/m^3

2. Calculate mass from densisty equation:

, then

We need to estimate the volume of the can to calculate the mass.

3. Estimate volume using differentials:

Cylinder volume equation is:

Considering that the can is an object with a hole inside, then we need to estimate the real volume of the sheet of steel.

Using differentials we have:

Then, we could say that

Replacing the values of d, h and dD, we obtain:

4. Calculate the mass

Convert volume unit into

Calculate mass

more than, less

less than, more