Question

Use differentials to estimate the amount of tin in a closed tin can with diameter 10 cm and height 15 cm if the tin is 0.04 cm thick. (Round your answer to two decimal places.)

Answer 1

try this:

the volume of the can is: \(\large V = \frac{\pi D^2}{4} \, h \)

so: \(dV = V_D \, dD + V_h \, dh\)

\( = \frac{\pi \, D}{2} \, h \, dD + \frac{\pi D^2 }{4} \, dh\)


\(\large dD = -\frac{0.04}{2} = -0.02, \, \, dh = -0.04\)