Question

a fish tank at an aquarium has a volume of 1,568 cubic feet and a depth of 8 feet. if the base of the tank is square, what is the length of each side of the tank?

Explanation:

Step1: Recall volume formula

The volume formula for a rectangular - prism (fish - tank) is $V = A\times h$, where $V$ is volume, $A$ is the area of the base, and $h$ is the height (depth). We know $V = 1568$ cubic feet and $h = 8$ feet.

Step2: Calculate base area

First, find the area of the base $A$. Rearranging the formula $A=\frac{V}{h}$. Substitute $V = 1568$ and $h = 8$ into the formula: $A=\frac{1568}{8}=196$ square feet.

Step3: Find side - length of square base

Since the base is square, and the area of a square is $A = s^{2}$, where $s$ is the side - length of the square. To find $s$, we take the square root of the area of the base. So $s=\sqrt{A}$. Substitute $A = 196$ into the formula: $s=\sqrt{196}=14$ feet.

Answer:

14 feet