Created by T Madas Question 262 (****+) y y = ( x − 4) C B A y=4 x O The diagram above shows the curve with equation y = ( x − 4) , x ∈ » , intersected by the straight line with equation y = , at the points A and B The curve meets the y axis at the point C Calculate the exact area of the shaded region, bounded by the curve and the straight line segments AB and BC C2P , area = 76 Created by T Madas Created by T Madas Question 263 (****+) x cm cm x cm The figure above shows the design of coffee jar with a “push on” lid The jar is in the shape of a right circular cylinder of radius x cm It is fitted with a lid of width cm , which fits tightly on the top of the jar, so it may be assumed that it has the same radius as the jar The jar and its lid is made of sheet metal and there is no wastage The total metal used to make the jar and its lid is 190π cm (This figure does not include the handle of the lid which is made of different material.) a) Show that volume of the jar, V cm3 , is given by ( ) V = π 95 x − x − x3 b) Determine by differentiation the value of x for which V is stationary [continues overleaf] Created by T Madas Created by T Madas [continued from overleaf] c) Show that the value of x found in part (b) gives the maximum value for V d) Hence determine the maximum volume of the jar MP1-X , x = cm , Vmax = 300π ≈ 942 cm3 Created by T Madas