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.
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:
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` .