How many gallons of water,on average, does each exhibit in the aquarium have?

Question

The Tennessee Aquarium in Chattanooga, Tennessee is the largest freshwater aquarium in the world with 450,000 gallons of water in 24 exhibits. The 130,000 square feet of the aquarium are home to more than 9000 creatures. An interesting fact is that 300,000 crickets, about 400,000 worms, and 15,000 pounds of seafood are devoured by the aquariums wildlife each year.

1. How many gallons of water,on average, does each exhibit in the aquarium have?

2. Suppose the tennessee Aquarium is opening a new saltwater exhibit that will have tropical fish from around the world. Three of the new rectangular aquariums being ordered are described below:

Aquarium one(180-gallon tank): The aquarium has a length of x inches, a height and width that are both 48 inches less than the length, and a volume of 41,472 cubic inches. Write a polynomial in standard form to describe the volume of the aquarium. The find its dimensions.

Aquarium two (300-gallon tank): The aquarium has dimensions of x feet long,(x-6)feet wide, and (x-5.5)feet high. The volume of the aquarium is 40 cubic feet. write a polynomial in standard form to describe the volume of the aquarium. Then find its dimensions.

Aquarium three(125- gallon tank): The length of this aquarium is three times its height and its width is 4 inches more than the height. The volume of the aquarium is 28,800 cubic inches. Write a polynomial in standard form to describe the volume of the aquarium. then find its dimensions.

Answer 1

1. 450,000 gallons in 24 exhibits

Assuming each exhibit is of the same size, then 450,000 ÷ 24 = 18,750 gallons per exhibit

 

2A. We know that Volume = Length x Width x Height

Our unknown is the Length, L; then Width = L - 48", and Height = L - 48"

So, our formula will be L x (L - 48") x (L - 48") = 41,472in³

this expression will result in a cubic equation, the solution for which is not easy.

Please see https://www.youtube.com/watch?v=OuiFS1Wma2U for a method to solve cubic equations

 

When the equation is solved, L = 72", W = 24", and H = 24"

 

2B. This portion is of the same type as 2A, and the cubic equation will be L x (L - 6) x (L - 5.5) - 180g = 0

The solution of the cubic equation yields L = 10ft, W = 4ft, H = 4.5ft

 

2C. This portion is of the same type as 2A, and the cubic equation will be L = 3H, W = H + 4", and H,

resulting in 3H x (H + 4") x H - 28,800in³= 0

rewritten, the equation becomes 3H x (H² + 4H) - 28,800in³ = 0

the solution is H = 20", L = 60", and W = 24"