One cubic foot of water is equivalent to 7.48 gallons.

If the capacity of the fish tank is 100 gallons, find the maximum possible height for the fish tank. Round your answer to the nearest thousandth of an inch.

Show your work.



Answer :

To find the maximum possible height for a fish tank with a capacity of 100 gallons, we'll follow these steps:

### Step 1: Convert tank capacity from gallons to cubic feet

Given that 1 cubic foot of water is equivalent to 7.48 gallons, we need to convert the tank capacity of 100 gallons to cubic feet.

[tex]\[ \text{Tank capacity in cubic feet} = \frac{\text{Tank capacity in gallons}}{\text{Conversion factor}} \][/tex]

[tex]\[ \text{Tank capacity in cubic feet} = \frac{100 \text{ gallons}}{7.48 \text{ gallons per cubic foot}} \approx 13.369 \text{ cubic feet} \][/tex]

### Step 2: Calculate the height of the tank in feet using the volume

Assume the tank has a cubic shape, which simplifies our calculation. We can find the height [tex]\( h \)[/tex] by taking the cube root of the volume, considering that the volume of a cube is given by [tex]\( V = h^3 \)[/tex].

[tex]\[ h = \sqrt[3]{\text{Tank capacity in cubic feet}} \][/tex]

[tex]\[ h \approx \sqrt[3]{13.369} \approx 2.373 \text{ feet} \][/tex]

### Step 3: Convert the height from feet to inches

Since there are 12 inches in a foot, we need to convert the height from feet to inches.

[tex]\[ \text{Height in inches} = h \times 12 \][/tex]

[tex]\[ \text{Height in inches} \approx 2.373 \times 12 \approx 28.480 \text{ inches} \][/tex]

### Step 4: Round the height to the nearest thousandth of an inch

Finally, we round the height to the nearest thousandth of an inch.

[tex]\[ \text{Height in inches (rounded)} \approx 28.480 \text{ inches} \][/tex]

Therefore, the maximum possible height for the fish tank, rounded to the nearest thousandth of an inch, is approximately [tex]\( 28.480 \)[/tex] inches.