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A square piece of tin of side 18 cm is t...

A square piece of tin of side 18 cm is to be made into a box without top, by cutting a square from each corner and folding up the flaps to form the box. What should be the side of the square to be cut off so that the volume of the box is the maximum possible.

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x = 3 cm
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KUMAR PRAKASHAN-APPLICATION OF DERIVATIVES -EXERCISE - 6.5
  1. What is the maximum value of the function sin x + cos x ?

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  2. Find the maximum value of 2x^(3)-24x+107 in the interval [1, 3]. Find ...

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  3. It is given that at x = 1, the function x^(4)-62x^(2)+ax+9 attains its...

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  4. Find the maximum and minimum values of x+sin(2x) on [0, 2pi].

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  5. Find two numbers whose sum is 24 and whose product is as large as poss...

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  6. Find two positive numbers x and y such that x+y=60 and xy^(3) is maxim...

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  7. Find two positive numbers x and y such that their sum is 35 and the pr...

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  8. Find two positive numbers whose sum is 16 and the sum of whose cubes i...

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  9. A square piece of tin of side 18 cm is to be made into a box without t...

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  10. A rectangular sheet of tin 45 cm by 24 cm is to be made into a box wit...

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  11. Show that of all rectangles inscribed in a given fixed circle, the squ...

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  12. Show that the right circular cylinder of given surface and maximum vol...

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  13. Of all the closed cylindrical cans (right circular), of a given volume...

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

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  15. Prove that the volume of the largest cone that can be inscribed in a s...

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  16. Show that the right circular cone of least curved surface and given vo...

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  17. Show that the semi-vertical angle of the cone of the maximum volume an...

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  18. Show that semi - vertical angle of right circular cone of given surfac...

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  19. The point on the curve x^(2)=2y which is nearest to the point (0, 5) i...

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  20. For all real values of x, the minimum value of f(x)=(1-x+x^(2))/(1+x+x...

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