answer the question

A rectangular sheet of cardboard measuring 90 cm by 48 cm is to be used to make an open box. A square of width w cm is removed from each corner to make the net shown. 48m 90m (not to scale) 6 Write an expression for the area A of the base of the box in terms of w. @A (DA (90 2w) (48 2w) cm2 4 320 180w 96w + 4W2 cm2 4 320 276w + 4w2 cm2 0 A 9 Write an expression for the volume. V, of the box in terms of w. 0 V = 4 320w 2761422 + 4W3 9 Solve for the possible value(s) of w that could maximise the volume of the box. You may use the substitutions u = 4 320 276w + 4w2 and v = w. Q) w=10 36046w+w2=0 {x} w: 46+26 2 .x'; W: 72 0=(w10)(w36) @ w10=0,w36=O 0 w = 10, 36 0 Find the second derivative, V\" . 0 V\" = 24w 552 e The value of V\" when w = 10 is The value of V\" when w = 36 is Therefore, the volume of the box is maximised when w = _ b a 3+ () F173 a 3