A box, constructed from a rectangular metal sheet, is 21 cm by 16cm by cutting equal squares of sides `x` from the corners of the sheet and then turning up the projected portions. The value of `x` os that volume of the box is maximum is (a)` 1` (b) ` 2` (c) `3` (d)` 4`

A rectangular sheet of tin 45 cm by 24 cm is to be made into a box without top, by cutting off square from each corner and folding up the flaps. What should be the side of the square to be cut off so that the volume of the box is maximum ?

An open box is to be made from a square piece of material, 24 cm on a side, by cutting equal squares from the corners and turning up the sides as shown in figure. Express volume V of the box as a function of x.

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.

We have a 12 square unit piece of thin material and want to make an open box by cutting small squares from the corners of our material and folding the sides up. The question is, which cut produces the box of maximum volume ?

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.

If the function f(x)=x^4+b x^2+8x+1 has a horizontal tangent and a point of inflection for the same value of x then the value of b is equal to -1 (b) 1 (c) 6 (d) -6

The rate of change of the volume of a sphere w.r.t. its surface area, when the radius is 2 cm, is 1 (b) 2 (c) 3 (d) 4

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

The lien x/3+y/4=1 meets the y- and x-a x y s at Aa n dB , respectively. A square A B C D is constructed on the line segment A B away from the origin. The coordinates of the vertex of the square farthest from the origin are (7, 3) (b) (4, 7) (c) (6, 4) (d) (3, 8)