A dairy farm in Punjab wants to minimize the material used for an open cylindrical milk container of volume 125π m³. What should be the radius? A. 2.5 m B. 5 m C. 10 m D. 12.5 m Answer: B) 5 m Explanation: V = πr²h = 125π → h = 125/r². Area S = πr² + 2πrh = πr² + 2πr(125/r²) = πr² + 250π/r. S' = 2πr - 250π/r² = 0 → r³ = 125 → r = 5 m.

imo class 12 application of derivatives

A dairy farm in Punjab wants to minimize the material used for an open cylindrical milk container of volume 125π m³. What should be the radius?

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A dairy farm in Punjab wants to minimize the material used for an open cylindrical milk container of volume 125π m³. What should be the radius?

Answer: B) 5 m

Explanation: V = πr²h = 125π → h = 125/r². Area S = πr² + 2πrh = πr² + 2πr(125/r²) = πr² + 250π/r. S' = 2πr - 250π/r² = 0 → r³ = 125 → r = 5 m.

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