Answer:
The volume of the rock is 13.368 cubic feet.
Step-by-step explanation:
The volume of the rock (
), measured in gallons, is equal to the volume of the fish aquarium without the decorative rock (
) minus the volume of the fish aquarium with the decorative rock (
), both measured in gallons.
Since the water flow is at constant rate, the volume of the rock is expressed by the following equation:
![V_{r} = V' - V''](https://tex.z-dn.net/?f=V_%7Br%7D%20%3D%20V%27%20-%20V%27%27)
(1)
Where:
- Flow rate, measured in gallons per hour.
- Filling time of the fish aquarium without the decorative rock, measured in hours.
- Filling time of the fish aquarium with the decorative rock, measured in hours.
And the flow rate is:
![\dot V = \frac{2000\,gal}{10\,h}](https://tex.z-dn.net/?f=%5Cdot%20V%20%3D%20%5Cfrac%7B2000%5C%2Cgal%7D%7B10%5C%2Ch%7D)
![\dot V = 200\,\frac{gal}{h}](https://tex.z-dn.net/?f=%5Cdot%20V%20%3D%20200%5C%2C%5Cfrac%7Bgal%7D%7Bh%7D)
The flow rate is 200 gallons per hour.
If we know that
,
and
, then the volume of the rock is:
![V_{r} = \left(200\,\frac{gal}{h}\right)\cdot (10\,h-9.5\,h)](https://tex.z-dn.net/?f=V_%7Br%7D%20%3D%20%5Cleft%28200%5C%2C%5Cfrac%7Bgal%7D%7Bh%7D%5Cright%29%5Ccdot%20%2810%5C%2Ch-9.5%5C%2Ch%29)
![V_{r} = 100\,gal](https://tex.z-dn.net/?f=V_%7Br%7D%20%3D%20100%5C%2Cgal)
![V_{r} = 13.368\,ft^{3}](https://tex.z-dn.net/?f=V_%7Br%7D%20%3D%2013.368%5C%2Cft%5E%7B3%7D)
The volume of the rock is 13.368 cubic feet.