A square piece of tin of side 30 cm is to be made into a box without top by cutting a square from each corner and folding up the flaps to form a box. If the volume of the box is maximum, then its surface area (in cm 2 ) is equal to

Step-by-step solution

Given that, the side of square is 30   cm and x   cm squares are cut off. The required diagram is, Now the dimensions of the cuboid formed will be l x = 30 - 2 x , b x = 30 - 2 x and h x = x . The Volume of the cuboid will be V x = 30 - 2 x 2 x Now to get Maximum value, ⇒ d V x d x = 0 ⇒ 2 30 - 2 x - 2 x + 30 - 2 x 2 1 = 0 ⇒ 30 - 2 x - 4 x + 30 - 2 x = 0 On simplifying we get, ⇒ x = 15   cm ,   5   cm But x cannot be 15   cm as the volume becomes zero. Hence x =