MATH SOLVE

5 months ago

Q:
# 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?

Accepted Solution

A:

Answer:75 square feet Step-by-step explanation:The aquarium is designed to hold 62.5cubic feetSince the aquarium has a square base, assume the aquaruim is a square prismLet X be the lenghtLet y be the height x^2.y = 62.5y = 62.5x^2The area of each side of the aquarium is xy. Since there are four sides, the total area of the side= 4xyThe area of the bottom of the aquarium = x^2Total surface area = 4xy + x^2Put y = 62.5/x^2 into the total surface area equation A = 4x(62.5/x^2) + x^2A= 250/x + x^2Differentiate A with respect to xdA/dx = -250(x^-2) + 2xdA/dx = 00 = 2x - 250x^-22x = 250x^-22x =250/ x^22x^3 = 250x^3 = 250/2x^3 = 125x = cbrt (125)x = 5Put x= 5 into A = x^2 + 250x^-1A= 5^2 + 250(5^-1)A= 25 + 250/5A = 25 + 50A = 75 square feet