Answer:
75 square feet
Step-by-step explanation:
The aquarium is designed to hold 62.5cubic feet
Since the aquarium has a square base, assume the aquaruim is a square prism
Let X be the lenght
Let y be the height
x^2.y = 62.5
y = 62.5x^2
The area of each side of the aquarium is xy. Since there are four sides, the total area of the side= 4xy
The area of the bottom of the aquarium = x^2
Total surface area = 4xy + x^2
Put y = 62.5/x^2 into the total surface area equation
A = 4x(62.5/x^2) + x^2
A= 250/x + x^2
Differentiate A with respect to x
dA/dx = -250(x^-2) + 2x
dA/dx = 0
0 = 2x - 250x^-2
2x = 250x^-2
2x =250/ x^2
2x^3 = 250
x^3 = 250/2
x^3 = 125
x = cbrt (125)
x = 5
Put x= 5 into A = x^2 + 250x^-1
A= 5^2 + 250(5^-1)
A= 25 + 250/5
A = 25 + 50
A = 75 square feet
