The storage of radioactive waste is an important problem in the nuclear industry. One problem that scientists must take into

account is volumetric expansion.

Consider a $40\mathrm{.}0$ gallon cylindrical metal drum of with a $22\mathrm{.}0-$inch diameter that is filled with a radioactive waste possessing a

coefficient of volume expansion of $9\mathrm{.}60{10}^{-4}{C}^{-1}.$ This drum will be filled at room temperature, $23\mathrm{.}0C,$ and then lowered

deep into the Earth, where temperatures can reach $125C,$ for storage.

The coefficient of volume expansion of the metal is $4\mathrm{.}10{10}^{-5}{C}^{-1}.$

What volume $V$ of waste, in gallons, will spill if the lid

becomes loose?

$V=$