Question

An open-topped glass aquarium with a square base is designed to hold ~62.5~ 62.5 space, 62, point, 5, space cubic feet of water. What is the minimum possible exterior surface area of the aquarium?

Answer 1

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