Chapter A.10, Problem 111AYU

(a)

To determine

To find: The no. of gallons of a gasoline when height of gasoline is given $12$ inches.

Answer to Problem 111AYU

The no. of gallons is $15660\cdot 42\text{gallon}$ .

Explanation of Solution

Given:

The volume $V$ of gasoline in the tank is given as:

  $V=40h^2\sqrt{\frac{96}{h}-0\cdot 608}$

Where $h$ is the height of the gasoline.

The given volume after substituting the value of $h$ is calculated as:

  $\begin{array}{c}V=40{\left(12\right)}^2\sqrt{\frac{96}{12}-0\cdot 608}\\ =15660\cdot 42\text{gallon}\end{array}$

(b)

To determine

To find: The no. of gallons of a gasoline when height of gasoline is given $1$ inches.

Answer to Problem 111AYU

The no. of gallons is $390\cdot 67\text{gallon}$ .

Explanation of Solution

Given:

The volume $V$ of gasoline in the tank is given as:

  $V=40h^2\sqrt{\frac{96}{h}-0\cdot 608}$

Here, $h$ is the height of the gasoline.

The given volume after substituting the value of $h$ is calculated as:

  $\begin{array}{c}V=40{\left(1\right)}^2\sqrt{\frac{96}{1}-0\cdot 608}\\ =390\cdot 67\text{gallon}\end{array}$