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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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.