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

Answer 1

we know that

The volume of the tank is equal to

$V=B*h$

where

B is the area of the base of the tank

h is the deep of the tank

In this problem we have

$V=1,568\ ft^{3}\\h=8\ ft$

$V=B*h$

Solve for B

$B=V/h$

substitute the values

$B=1,568/8$

$B=196\ ft^{2}$ -------> area of the base of the tank

we know that

the base of the tank is a square

the area of a square is

$A=x^{2}$

where

x is the length side of the square

$196=x^{2}$

$x=14\ ft$

therefore

the answer is

the length of each side of the base of the tank is $14\ ft$

Answer 2

If the base of the tank is a square, then the length and width are the same, making the area length*width*height=length*length*8=length^2*8=1268. Dividing both sides by 8, we get length^2=158.5 and by square rooting both sides we get length=sqrt(158.5)=around 12.6 for the length (and width), and 8 feet for the depth/height