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Question : 17
Total: 29
An open tank with a square base and vertical sides is to be constructed from a metal sheet so as to hold a given quantity of water. Show that the cost of material will be least when depth of the tank is half of its width. If the cost is to be borne by nearby settled lower income families, for whom water will be provided, what kind of value is hidden in this question?
Solution:
Let length, width and depth of the tank will be l, l and h respectively.
Volume of the tank =I 2 h
V =I 2 h
Total surface area =I 2
S =I 2
S =I 2
⇒
2l -
⇒I 3
⇒ I = 2h from (i)
Hence,cost material will be least when the depth of the tank is half of its width.
If surface area of the sheet is minimum then the cost of sheet will be less, hence, making the tank economical as well as cost-effective. Also people can come together to solve their common problems, which will be difficult if they try to solve it individually.
Volume of the tank =
V =
Total surface area =
S =
S =
⇒
2l -
⇒
⇒ I = 2h from (i)
Hence,cost material will be least when the depth of the tank is half of its width.
If surface area of the sheet is minimum then the cost of sheet will be less, hence, making the tank economical as well as cost-effective. Also people can come together to solve their common problems, which will be difficult if they try to solve it individually.
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