Q. 65 - Calculus

Question

Suppose a large oil tank develops a hole that causes oil

to leak from the tank at a rate of $r\left(t\right) = 0.05t$ gallons

per hour. Construct and then solve a definite integral to

determine the amount of oil that has leaked from the tank

after one day.

Step-by-Step Solution

Answer

$14.4$ gallons oil leaked in a day

Step 1. Given information

Leaking volume equation is given as $r\left(t\right)=0.05 t$

Step 2. Oil leaked in a day

The integral is for one day is ${\int }_0^{24}0.05tdt$

Now simplify it as,

$$\begin{gathered} {\int }_0^{24}0.05tdt \\ =0.05{\left[\frac{t^2}{2}\right]}_0^{24} \\ =0.05\left(\frac{(24{)}^2}{2}\right) \\ =0.05\left(288\right) \\ =14.4 \\ =14.4 \mathrm{gallons} \end{gathered}$$