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. 48cm 90cm (not to scale) 6 Write an expression for the area A of the base of the box in terms of w. @A A 0A (90 2w) (48 2w) cm2 4 320 180w 96w + 4w2 cm2 4 320 276w + 4W2 cm2 6 Write an expression for the volume. V, of the box in terms of w. 0 V = 4 320w 276w2 + 4W3 e 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 CV) 36046w+w2=0 {x5 w=46+26 2 w _2 ... W 2 O=(w10)(w36) @ w10=0,w36=0 o w=10, 36 \f6 The value of V' when w = 10 is 312. The value of V\" when w = 36 is 312. Therefore, the volume of the box is maximised when w = 10. Hence state the dimensions of the box with the maximum volume. Length = C] cm Width = C] cm Height = C] cm X+