pre Complete tasks a), b) and c) on clean lined paper, make sure you show all working and attach units to your final answers. This is to be submitted on our first week back after Christmas. a) A metal cube of sides 15 cm is melted down and cast into a solid sphere, calculate: i) the surface area and volume of the cube, ii) the surface area of the sphere. b) For the rivet with dimensions shown below in mm, find: i) the total surface area of the rivet, ii) the volume of the metal in m required to manufacture 1500 rivets. Note: consider the top part of the rivet as a hemisphere. 10 15 06 c) You work for a company that has been asked to manufacture a prototype hopper [see below]. The tapered part is in the shape of a frustum of a cone and the dimensions are given in mm Neglecting the thickness of material, determine: i) the outer surface area of the hopper in mm 2 and convert this to m ii) the hopper's volume in mm 3 and convert this to m Note: Round the values to 2 decimal places. 3 2 230 180 100 ! 050