Created by T Madas Question 247 (****+) 12x H G D C y E F x A B 10x The figure above shows the design of a baking tray with a horizontal rectangular base ABCD , measuring 10x cm by y cm The faces ABFE and DCGH are isosceles trapeziums, parallel to each other The lengths of the edges EF and HG are 12x cm The faces ADHE and BCGF are identical rectangles The height of the tray is x cm The capacity of the tray is 1980 cm3 a) Show that the surface area, A cm , of the tray is given by A = 22 x + 360 5+ x ( ) b) Determine the value of x for which A is stationary, showing that this value of x minimizes the value for A c) Calculate the minimum surface area of the tray SYN-K , x ≈ 3.744 , Amin ≈ 925 [solution overleaf] Created by T Madas Created by T Madas Created by T Madas Created by T Madas Question 248 (****+) y y = x − 8x A O x R L1 L2 The figure above shows the graph of the curve C with equation y = x − 8x , x ≥ The curve meets the x axis at the origin O and at the point A The tangent to C at O is denoted by L1 and the tangent to C at A is denoted by L2 The finite region R , shown shaded in the figure above, is bounded by C , L1 and L2 Determine the area of R 384 ≈ 11.0 35 Created by T Madas