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A rectagular sheet of fixed permeter with sides having thir lengths in the ratio 8 : 15 is converted into an open revtangular bx by foldings after removing squares of equal area from all four couners.If the total area of removed squareis 100 , the resulting box has macimum value,the dimensions of the sides of the rectangular sent are

A

24

B

32

C

45

D

60

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The correct Answer is:
A, C
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A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8 : 15 is converted into an open rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. The lengths of the sides of the rectangular sheet are :

A rectangular sheet of fixed perimeter with sides having their lengths in the ratio 8: 15 is converted into anopen rectangular box by folding after removing squares of equal area from all four corners. If the total area of removed squares is 100, the resulting box has maximum volume. Then the length of the sides of the rectangular sheet are 24 (b) 32 (c) 45 (d) 60

A box open from top is made from a rectangular sheet of dimension a xx b by cutting squares each of side x from each of the four corners and folding up the flaps. If the volume of the box is maximum, then x is equal to :

An open topped box is to be constructed by removing equal squares from each corner of a 3 metre by 8 metre rectangular sheet of aluminium and folding up the sides.Find the volume of the largest such box.

Four identical strips in the form of right isosceles triangles are removed from the four corners of a square sheet of side 8 cm. Find the area of the remaining sheet, if the length of each, equal sides of the triangles is 4 cm,

A box of maximum volume with top open is to be made by cutting out four equal squares from four corners of a square tin sheet of side length a feet and then folding up the flaps. Find the side of the square cut-off.

From a rectangular sheet of dimensions 30cm times 80cm , four equal squares of side x cm are removed at the corners, and the sides are then turned up so as to form an open rectangular box. Find the value of x so that the volume of the box is the greatest.

An open box is be made from a rectangular cardboard of sides 35 cm and 20 cm, by cutting equal squares from each corner and then bending up the edges. If the base area of box thus formed is 250 cm^(2) , find the length of the side of the square cut from each corner.

ARIHANT MATHS-MONOTONICITY MAXIMA AND MINIMA-Exercise (Questions Asked In Previous 13 Years Exam)
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  2. The fuction f(x)=2|x|+|x+2|-||x+2|-2|x|} has a local minimum or a loca...

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  3. A rectagular sheet of fixed permeter with sides having thir lengths in...

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  4. A vertical line passing through the point (h, 0) intersects the ellips...

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  5. Let f,g and h be real-valued functions defined on the interval [0,1] b...

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  6. e total number of local maxima and local minima of the function f(x) =...

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  7. If the function g:(-oo,oo)->(-pi/2,pi/2) is given by g(u)=2tan^-1(e^u)...

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  8. The second degree polynomial f(x), satisfying f(0)=o, f(1)=1,f'(x)gt...

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  9. If f(x)=x^(3)+bx^(2)+cx+dand 0 ltb^(2)ltc, then in (-oo,oo)

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  10. If f(x)=x^(2)+2bx+2c^(2)and g(x)=-x^(2)-2cx+b^(2), such that minf(x)gt...

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  11. The length of a longest interval in which the function 3sinx-4sin^(3...

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  12. If f(x)=e^(1-x) then f(x) is

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  13. The maximum value of (cosalpha(1))-(cos alpha(2))...(cosalpha(n)), u...

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  14. If f(x) = {{:(e ^(x),,"," 0 le x lt 1 ,, ""), (2- e^(x - 1),,"," 1 lt ...

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  15. If f(x) is a cubic polynomil which as local maximum at x=-1 . If f(2)=...

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  16. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  17. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  18. Consider the function f:(-oo, oo) -> (-oo ,oo) defined by f(x) =(x^2...

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  19. For the circle x^(2)+y^(2)=r^(2), find the value of r for which the ar...

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  20. Find a point on the curve x^2 + 2y^2 = 6, whose distance from the li...

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