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CBSE Class 12-science Answered

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 the material will be least when the depth of the tank is half of its width.
Asked by Manoj | 04 Sep, 2013, 04:41: AM
answered-by-expert Expert Answer
 
begin mathsize 16px style Let space length comma space width space and space depth space of space the space tank space be space straight l comma straight l space and space straight h space respectively. Volume space of space the space tank space equals space straight l squared straight h Total space surface space area space equals space straight l squared plus 4 lh straight v equals straight l squared straight h straight h equals straight v over straight l squared....... left parenthesis straight i right parenthesis Surface space area space equals space space straight l squared plus 4 lh straight S equals space straight l squared plus 4 straight l cross times straight v over straight l squared straight S equals space straight l squared plus 4 cross times straight v over straight l rightwards double arrow dS over dl equals 2 straight l minus fraction numerator 4 straight v over denominator straight l squared end fraction dS over dl equals 0 2 straight l minus fraction numerator 4 straight v over denominator straight l squared end fraction equals 0 rightwards double arrow straight l cubed equals 2 straight v rightwards double arrow straight l equals 2 straight h.......... from space left parenthesis straight i right parenthesis dS squared over dl squared equals 2 plus fraction numerator 8 straight v over denominator straight l cubed end fraction greater than 0 Hence comma space cost space material space will space be space least space when space the space depth space of space the space tank space is space half space of space its space width. end style
Answered by | 11 Dec, 2017, 02:05: PM

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CBSE 12-science - Maths
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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CBSE 12-science - Maths
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