Chapter 1, Problem 63RE

Solution

To write: The depth of the oil remaining in the tank $t$ seconds later as a function of $t$ .

The depth of the oil remaining in the tank $t$ seconds later is equal to $h=40-2t$ ft.

Given information:

A cylindrical tank with diameter $20$ ft is filled with oil to depth of $40$ feet.

Calculation:

The diameter of the cylindrical tank is $20$ ft.

Then the radius of the cylindrical tank is $10$ ft.

The depth is $40$ ft.

If the oil drains at a rate of $2$ cube ft per second, then after $t$ seconds, it will decrease $2t$ feet height. Therefore, the depth of the oil remaining after $t$ seconds is below:

  $h=40-2t$

Hence, the depth of the oil remaining in the tank $t$ seconds later is $40-2t$ ft.