Question

An aquarium is 0.5 feet wide, 1.5 feet tall, and 2 feet long.The bottom is covered with gravel to a height of 3 inches.The tank will be filled with water to 3 inches below the top.How many gallons of water are needed to fill the aquarium?(Use 1 gallon = 0.134 ft.) Ignore any water that might seepinto the layer of gravel. Round to the nearest tenth.

Answer 1

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,

`\text{ the base area of the tank }=2ft*0.5ft=1ft^2`

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

`\begin{gathered} x+(1)/(4)+(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}`

Therefore, the height of the water in the tank is 1 ft.

Step 3: Find the volume of the water in the tank

`\begin{gathered} \text{ the volume of the water is given by} \\ V=\text{ base area of the tank }*\text{ height of the water} \\ \text{ Where V is the volume of the water} \end{gathered}`

Therefore,

`V=1ft^2*1ft=1ft^3`

Since 1 gallon is equivalengt to 0.134 ft³ then

`V=(1)/(0.134)\text{gallons }=7.5\text{ gallons}`

Hence, the number of gallons of water are needed to fill the aquarium is 7.5 gallons.