Mathematics Higher Level Robert Joinson

©Sumbooks 2002Higher Level41. Similar Shapes1. Two hollow cylinders are similar in shape. One is12cm tall and the other is 18cm tall.Calculate the ratio ofa) the areas of their endsb) their volumes.c) If the smaller one has a volume of 100 cm 3 , what isthe volume of the larger one?2. A cone of height 3h is cut into two parts to make a smaller cone ofheight 2h.a) What is the ratio of the volumes of the two parts?b) If the surface area of the top part is 200 cm 2 , what was thesurface area of the original cone?3. Two similar blocks of metal made from the same material have atotal surface area of 25 cm 2 and 64 cm 2 . If the smaller one has amass of 30 grams, what is the mass of the larger one?2hh4. A ball has a diameter of 8cm and weighs 200 grams. Calculate the weight of a ball of 10cmdiameter made from the same material.5. A cylindrical can of height 15cm holds one litre of orange juice. What height, to the nearestmm, must a similar can be if it holds 500ml?6. Two similar cones have heights of 100cm and50cm. If the volume of the smaller one is1000 cm 3 , calculate the volume of the larger one.7. Two similar boxes have correspondingsides of 6cm and 4cm.a) If the surface area of the smaller boxis 50 cm 2 , what is the surface area ofthe larger box?b) If the volume of the larger box is50 cm 3 , what is the volume of thesmaller box?6cm4cm8. Two similar cornflakes packets have widths of 25cm and 20cm. Cornflakes are sold inpackets of 750g, 500g and 350g. If the 25cm packet holds 750g, how much does the 20cmpacket hold?