Finding the Amount of Gasoline in a Tank

A Shell station stores its gasoline in an underground tank that is a right circular cylinder lying on its side. The volume \(V\) of gasoline in the tank (in gallons) is given by the formula \[ V( h) =40h^{2}\sqrt{\dfrac{96}{h}-0.608} \] where \(h\) is the height (in inches) of the gasoline as measured on a depth stick. See Figure 5.

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1. If \(h=12\) inches, how many gallons of gasoline are in the tank?
2. If \(h=1\) inch, how many gallons of gasoline are in the tank?

Solution (a) We evaluate \(V\) when \(h=12.\) \[ V( 12) =40 ( 12) ^{2} \sqrt{\dfrac{96}{12}-0.608}=40\cdot 144 \sqrt{8-0.608}=5760 \sqrt{7.392}\approx 15{,}660 \]

There are about 15,660 gallons of gasoline in the tank when the height of the gasoline in the tank is 12 inches.

(b) Evaluate \(V\) when \(h=1.\) \[ V( 1) =40 ( 1) ^{2} \sqrt{\dfrac{96}{1}-0.608}=40 \sqrt{96-0.608}=40 \sqrt{95.392}\approx 391 \]

There are about \(391\) gallons of gasoline in the tank when the height of the gasoline in the tank is 1 inch.