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.
