Question

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

Answer 1

Answer:

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:

$\rho=\frac{m}{v}$, then $m=\rho .v$

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

3. Estimate volume using differentials:

Cylinder volume equation is:

$V=\frac{1}{4}\pi d^{2}h$

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:

$dV=\frac{1}{2}\pi Dh (dD)$

Then, we could say that $dD=0.013 cm$

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

$dV=\frac{1}{6}\pi (6 cm)(11 cm)(0,013 cm)$

$dV=0,4492 cm^3$

4. Calculate the mass

Convert volume unit into $m^3$

$0,4492 cm^3x\frac{1 m^3}{1x10^6 cm^3} =0,4492 x 10^-6 m^3$

Calculate mass

$m=\rho .v$

$m=8000 \frac{kg}{m^3}.0,4492 x10^-6 m^3$

$m=0,00359 kg =3,59 g$