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` so that volume of the box is maximum is (a)` 1` (b) ` 2` (c) `3` (d)` 4`

A box is constructed from a rectangular metal sheet 21 cm by 16 cm cutting equal squares of sides x cm from the corners of the sheet and then turning up the projected portions. For what value of x the volume of the box will be maximum ?

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 ?

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 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.

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.

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 (a) 24 (b) 32 (c) 45 (d) 60

The value of lim_(x->pi)(1+cos^3x)/(sin^2x) is (a) 1/3 (b) 2/3 (c) -1/4 (d) 3/2

The three sides of a trapezium are equal, each being 8cm. The area of the trapezium, where it is maximum, is (a) 24sqrt(3) c m^2 (b) 48sqrt(3)c m^2 (c)72 sqrt(3)c m^2 (d) none of these

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 the removed squares is 100, the resulting box has maximum volume. The lengths of the side of the rectangular sheet are

The maximum value of f(x)=x/(1+4x+x^2) is -1/4 (b) -1/3 (c) 1/6 (d) 1/6