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A conical tank is of height 12 m and surface diameter 8 m. Water is pumped into the tank at the rate of 50 m'/min. How fast is the water level increasing when the depth of the water is 6 m? . A cylindrical container of radius r and height h has a constant volume V. The cost of the materials for the surface of both of its ends is twice the cost of its sides. State h in terms of rand V. Hence, find h and r in terms of V such that the cost is minimum.

A conical tank is of height 12 m and surface diameter 8 m. Water is pumped into the tank at the rate of 50 m'/min. How fast is the water level increasing when the depth of the water is 6 m? . A cylindrical container of radius r and height h has a constant volume V. The cost of the materials for the surface of both of its ends is twice the cost of its sides. State h in terms of rand V. Hence, find h and r in terms of V such that the cost is minimum.

Mathematics For Machine Technology
Mathematics For Machine Technology
8th Edition
ISBN:9781337798310
Author:Peterson, John.
Publisher:Peterson, John.
Chapter47: Applications Of Formulas To Cutting Speed, Revolutions Per Minute, And Cutting Time
Section: Chapter Questions
Problem 41A: Compute the following problems. Express the answers to 1 decimal place. Use: T=LFN A slot 812.00...
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27 a. A conical tank is of height 12 m and surface diameter 8 m. Water is pumped into the tank at the rate of 50 m' /min . How fast is the water level increasing when the depth of the water is 6 m? b. A cylindrical container of radius r and height h has a constant volume V. The cost of the materials for the surface of both of its ends is twice the cost of its sides. State h in terms of r and V. Hence, find h and r in terms of V such that the cost is minimum.
Transcribed Image Text:27 a. A conical tank is of height 12 m and surface diameter 8 m. Water is pumped into the tank at the rate of 50 m' /min . How fast is the water level increasing when the depth of the water is 6 m? b. A cylindrical container of radius r and height h has a constant volume V. The cost of the materials for the surface of both of its ends is twice the cost of its sides. State h in terms of r and V. Hence, find h and r in terms of V such that the cost is minimum.
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