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 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.

A metallic sheet is of rectangular shape with dimensions 48cmxx36cm . An open box is made by cutting off squares of side 8 cm from each and folding up the flaps. Find the volume of the 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 24 (b) 32 (c) 45 (d) 60

An open box is to be made of a square sheet of tin with side 20 cm, by cutting off small squares from each comer and folding the flaps. Find the side of small square, which is to be cut off, so that volume of box is maximum.

A square ·piece of tin of side 12 cm is to be made into a box without a top by cutting a square from each corner and folding up the flaps to form a box. What should be the side of square to be cut off'. so that the volume of box is maximum and also find the volume of box.