Question

Use differentials to estimate the amount of metal in a closed cylindrical can that is 10 cm high and 10 cm in diameter if the metal in the top and the bottom is 0.2 cm thick and the metal in the sides is 0.05 cm thick. (Round your answer to two decimal places.)

Answer 1

dV = 32.98 cm³

Step-by-step explanation:

We know that

V = f ( h,r)

`dV= (\partial V)/(\partial r)dr+ (\partial V)/(\partial h)dh`

We also know that

`V=\pi r^2h`

`dV= 2\pi h dr + \pi r^2 dh`

Given that

h= 10 cm

d=10 cm , r= 5 cm

Thickness = 0.05 cm so dr = 0.05 cm

The metal in the top and the bottom is 0.2 cm thick so dh = 0.2 + 0.2 cm

dh = 0.4 cm

Now by putting the values

`dV= 2\pi h dr + \pi r^2 dh`

`dV= 2* \pi * 5* 0.05 + \pi * 5^2* 0.4\ cm^3`

dV = 32.98 cm³