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.

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 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 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 ?

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 ?

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 tank with rectangular base and rectangular sides, open at the top is to be constructed so that its depth is 2 m and volume is 8 m^(3) . If building of tank costs Rs 70 per sq metres for the base and Rs 45 per square metre for sides. What is the cost of least expensive tank?

A closed box (cuboid) with a square base is to have a volume 2000c.c, The material for the top and bottom of the box is to cost Rs 3 per square cm and the material for the sides is to cost Rs 1.50 per square cm. If the cost of the material is to be least find the dimension of the box.

Water is filled in a rectangular tank of size 3mxx2mxx1m . a) Find the total force exerted by the water on the bottom surface of the tank. b) Consider a vertical side of area 2mxx1m . Take a horizontal strip of wide deltax metre in this side, situated at a depth of x metre from the surface of water.Find the force by the water on this strip. c) Find the torque of the force calculate in part b) about the bottom edge of this side. d) Find the total force by the water on this side. e) Find the total torque by the water on the side about the bottom edge. neglect the atmospheric pressure and take =10ms^-2 .