The height of a cylindrical tank is 9.5 feet. The diameter of this tank 1.5 feet longer than the height. The tank was holding water at full capacity, but someone consumed one-seventh of the water. Which is closest to the volume of the remaining water in the tank?

To solve this problem we first need to calculate the volume of the tank at full capacity, since it is a cylinder we can use the appropriate formula shown below:

volume = pi*r²*h

Where r is half the diameter. Since the diameter of this tank is 1.5 feet longer than the height and the height is 9.5 feet, then the diameter is equal to 11 feet, so the radius must be r = 11/2 = 5.5 feet. We can now use the formula:

volume = pi*(5.5)²*9.5 = 902.815 feet³

Since someone consumed 1/7 of the water, the remainder must be 6/7 of the total volume. So we have:

remainder volume = (6/7)*volume = (6/7)*902.815 = 773.841 feet³

xero099 xero099 · Answer 2 · 2020-05-17T02:16:23+02:00

xero099 xero099

17-05-2020

Answer:

[tex]V_{r} = 773.841\,ft^{3}[/tex]

Step-by-step explanation:

The full capacity of the tank is now computed:

[tex]V = \frac{\pi}{4} \cdot (11\,ft)^{2}\cdot (9.5\,ft)[/tex]

[tex]V \approx 902.815\,ft^{3}[/tex]

The volume of the remaining water in the tank is:

[tex]V_{r} = \left(1-\frac{1}{7} \right)\cdot (902.815\,ft^{3})[/tex]

[tex]V_{r} = \frac{6}{7}\cdot (902.815\,ft^{3})[/tex]

[tex]V_{r} = 773.841\,ft^{3}[/tex]

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