Answer:
20.25 more gallons
Step-by-step explanation:
To find out how many more gallons of water it will take to fill the tank, we first need to calculate the volume of the tank when it's full, then determine how much water is already in the tank, and finally find the difference.
Given:
Full tank dimensions:
Length = 2.25 ft = 12 ft × 2.25 in/ft = 27 in.,
Width = 1.75 ft = 12 ft × 1.75 in/ft = 21 in.
Height = 11 in.
The tank is 25% full.
Volume of the Tank:
The volume [tex] V_{\textsf{full}} [/tex] of the tank when it's full is given by:
[tex] V_{\textsf{full}} = \textsf{Length} \times \textsf{Width} \times \textsf{Height} [/tex]
Substitute the given values:
[tex] V_{\textsf{full}} = 27\times 2 1 \times 11 [/tex]
[tex] V_{\textsf{full}} = 6237 \, \textsf{in}^3 [/tex]
Volume of Water Already in the Tank:
Since the tank is 25% full, the volume of water already in the tank is 25% of the volume of the full tank.
[tex] \textsf{Volume of water already in the tank} = \dfrac{25}{100} \times V_{\textsf{full}} [/tex]
[tex] \textsf{Volume of water already in the tank} = 0.25 \times V_{\textsf{full}} [/tex]
[tex] \textsf{Volume of water already in the tank} = 0.25 \times 6237 [/tex]
[tex] \textsf{Volume of water already in the tank} = 1559.25 \, \textsf{in}^3 [/tex]
Volume of Water Needed to Fill the Tank:
The volume of water needed to fill the tank is the difference between the volume of the full tank and the volume of water already in the tank.
[tex] \textsf{Volume of water needed} = V_{\textsf{full}} - \textsf{Volume of water already in the tank} [/tex]
[tex] \textsf{Volume of water needed} = 6237 - 1559.25 [/tex]
[tex] \textsf{Volume of water needed} = 4677.75 \, \textsf{in}^3 [/tex]
Now, since [tex]1 \, \textsf{gallon} = 231 \, \textsf{in}^3[/tex], we need to convert the volume to gallons:
For this divide volume by 231.
[tex] \textsf{Volume in gallons} = \dfrac{4677.75 }{ 231} [/tex]
[tex] \textsf{Volume in gallons} = 20.25 [/tex]
Thus, it will take approximately 20.25 more gallons of water to fill the tank.
