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Sagot :
Step 1: Find the base area of the tank.
The base of the tank is a rectangle of length 2 ft and width 0.5 ft.
Hence,
[tex]\text{ the base area of the tank }=2ft\times0.5ft=1ft^2[/tex]Step 2: Find the height of the water in the tank.
The height of the tank = 1.5ft
the height of the gravel = 3in = 3/12 ft = 1/4 ft
The water is 3 inches (= 1/4 ft) below the top of the tank.
Hence, we must have that
[tex]\begin{gathered} x+\frac{1}{4}+\frac{1}{4}=1.5 \\ x+0.25+0.25=1.5 \\ x+0.5=1.5 \\ x=1.5-0.5=1\text{ ft} \end{gathered}[/tex]Therefore, the height of the water in the tank is 1 ft.
Step 3: Find the volume of the water in the tank
[tex]\begin{gathered} \text{ the volume of the water is given by} \\ V=\text{ base area of the tank }\times\text{ height of the water} \\ \text{ Where V is the volume of the water} \end{gathered}[/tex]Therefore,
[tex]V=1ft^2\times1ft=1ft^3[/tex]Since 1 gallon is equivalengt to 0.134 ft³ then
[tex]V=\frac{1}{0.134}\text{gallons }=7.5\text{ gallons}[/tex]Hence, the number of gallons of water are needed to fill the aquarium is 7.5 gallons.
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