Question

1. higher order thinking 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 the volume formula for a rectangular prism (fish tank).

The volume \( V \) of a rectangular prism is given by \( V = l \times w \times h \), where \( l \) is length, \( w \) is width, and \( h \) is height (depth here). Since the base is square, \( l = w \), let's call this side length \( s \). So the volume formula becomes \( V = s \times s \times h = s^2h \).

Step2: Substitute the known values into the formula.

We know \( V = 1568 \) cubic feet and \( h = 8 \) feet. Substituting these into \( V = s^2h \), we get \( 1568 = s^2 \times 8 \).

Step3: Solve for \( s^2 \).

Divide both sides of the equation by 8: \( s^2=\frac{1568}{8} \). Calculating the right side, \( \frac{1568}{8} = 196 \).

Step4: Solve for \( s \).

Take the square root of both sides: \( s = \sqrt{196} \). Since \( 14 \times 14 = 196 \), \( s = 14 \).

Answer:

The length of each side of the tank is 14 feet.