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A square-based tank of capacity 250 cu m...

A square-based tank of capacity 250 cu m has to bedug out. The cost of land is Rs 50 per sq m. The cost of digging increases with the depth and for the whole tank the cost is Rs `400 xx (depth)^2`. Find the dimensions of the tank for the least total cost.

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The correct Answer is:
10 metre, 10 metre, 2.5 metre
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NAGEEN PRAKASHAN-APPLICATIONS OF DERIVATIVES-Exercise 6g
  1. If x+y=1 then find the maximum value of the function xy^2

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  2. Find two number whose sum is 100 and the sum of twice of first part an...

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  3. Find two numbers whose sum is 12 and the product of the square of one ...

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  4. Divide 15 into two parts such that product of square of one part and c...

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  5. (i) The two sides of a rectangle are x units and (10 - x) units. For w...

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  6. Show that the triangle of maximum area that can be inscribed in a give...

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  7. If the surface area of an open cylinder is 100 cm^(2), prove that it...

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  8. (i) The base of an open rectangular box is square and its volume is 2...

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  9. An open tank of square base is to be constructed which has a given qua...

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  10. The base of a cuboid is square and its volume is given. Show that its...

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  11. Find the maximum are of the isosceles triangle inscribed in the ell...

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  12. The volume of a closed square based rectangular box is 1000 cubic metr...

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  13. Show that height of the cylinder of greatest volume which can be insc...

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  14. The sum of perimeter of a square and circumference of a circle is give...

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  15. A square-based tank of capacity 250 cu m has to bedug out. The cost of...

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  16. The stiffness of a beam of rectangular cross-section varies as the pr...

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  17. The expenditure on fuels in running a train varies as the square of it...

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  18. The combined resistance of two resistors R(1) and R(1)" is given by "1...

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  19. Prove that the area of right-angled triangle of given hypotenuse is...

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  20. A wire of length 28 m is to be cut into two pieces. One of the piec...

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