Created by T Madas Question 221 (****) 2c h r The figure above shows solid right prism of height h cm The cross section of the prism is a circular sector of radius r cm , subtending an angle of radians at the centre a) Given that the volume of the prism is 1000 cm3 , show clearly that S = 2r + 4000 , r where S cm is the total surface area of the prism b) Hence determine the value of r and the value of h which make S least, fully justifying your answer C2P , r = 10 , h = 10 Created by T Madas Created by T Madas Question 222 (****) A curve has equation y = x2 − x x +2, x∈» , x ≥ Find the coordinates of the stationary points of the curve and classify them as local maxima, local minima or a points of inflexion MP1-X , local minimum at ( 8, −30 ) , local maximum at ( 0, ) Created by T Madas Created by T Madas Question 223 (****) y y = 27 x − x P O x The figure above shows the curve C with equation y = 27 x − x , x ≥ The curve meets the x axis at the origin O and at the point P a) Find the exact x coordinate of P b) Calculate the gradient of C at the point P dy = − 81 x=9 , dx Created by T Madas