Question

rectangular sheet of dimensions 30cmx80cm four equal squares of side xcm are removed at the corners and the sides are then turned up so as to form an open rectangular box find the value of x so that rhe volume of the box is the greatest. please guide me the correct answer​

Answer 1

Answer:

Length of the box = 80 – 2x = l Breadth of the box = 30 – 2x = b Height of the box = x = h

Volume = lbh = (80 – 2x) (30 – 2x). x

= x (2400 – 220x + 4x2) f(x) = 4x3 – 220x2 + 2400x f'(x) = 12x2 – 440x + 2400 = 4[3x2 – 110x + 600] f'(x) = 0 ⇒ 3x2 – 110x + 600 = 0 If x = 30, b = 30 – 2x = 30 – 2(30) = –30 < 0 ⇒ x ≠ 30 ∴ x = 20/3 f"(x) = 24x – 440

When x = 20/3, f"(x) = 24. 20/3 – 440 = 160 – 440 = –280 < 0 f(x) is maximum when x = 20/3 Volume of the box is maximum when x = 20/3 cm.

rectangular-sheet-of-dimensions-30-cm-80-cm-four-equal-squares-of-side-cms-are-removed