Use differentials to approximate the volume of the shell. The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the shell. ?? cm3...

Use differentials to approximate the volume of the shell.

The thickness of the shell is a = 0.5 centimeter. Use differentials to approximate the volume of the shell.

?? cm3


http://www.webassign.net/larcalc9/3-9-036-alt.gif


Expert Answers info

sciencesolve eNotes educator | Certified Educator

calendarEducator since 2011

write5,349 answers

starTop subjects are Math, Science, and Business

You need to use the formula that helps you to find the volume of sphere such that:

`V = (4/3)pi*r^3`

Notice that the problem provides the radius of sphere, hence, you need to substitute 100 for r such that:

`V =(4/3)pi*100^3`

You need to differentiate both sides such that:

`dV = ((4/3)pi*r^3) dr => dV = (4/3)*pi*3r^2 dr`

Reducing by 3 yields:

`dV = 4pi*r^2 dr`

Substituting the `0.5`  for `dr`  yields:

`dV = 4pi*100^2*0.5 => dV = 4pi*100*50 => dV = 20000pi~~ 62831.35 cm^3`

Hence, evaluating the volume of the shell, under the given conditions, yields `dV =~~ 62831.35 cm^3` .

check Approved by eNotes Editorial

Unlock This Answer Now