MHT CET 2024 Mathematics question

Mathematics Application of Derivatives MHT CET 2024

An open tank with a square bottom, to contain 4000 cubic cm. of liquid, is to be constructed. The dimensions of the tank, so that the surface area of the tank is minimum, are

(A)side of square bottom = 40 cm, height = 10 cm.
(B)side of square bottom = 20 cm, height = 10 cm.Correct
(C)side of square bottom = 10 cm, height = 40 cm.
(D)side of square bottom = 5 cm, height = 160 cm.

Answer: (B)

Solution

Let the side of the square base be and the height . Volume: . The tank is open, so the surface area is base plus four walls: . Then .

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Question ID VK-095509