text: # Resources tagged with: Spheres, cylinders & cones
  
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  ### There are 21 results
  
  Broad Topics > 3D Geometry, Shape and Space > Spheres, cylinders & cones
  
  ### Tin Tight
  
  ##### Age 14 to 16Challenge Level
  
  What's the most efficient proportion for a 1 litre tin of paint?
  
  ### Conical Bottle
  
  ##### Age 14 to 16Challenge Level
  
  A right circular cone is filled with liquid to a depth of half its vertical height. The cone is inverted. How high up the vertical height of the cone will the liquid rise?
  
  ### Funnel
  
  ##### Age 14 to 16Challenge Level
  
  A plastic funnel is used to pour liquids through narrow apertures. What shape funnel would use the least amount of plastic to manufacture for any specific volume ?
  
  ### Cola Can
  
  ##### Age 11 to 14Challenge Level
  
  An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
  
  ### Peeling the Apple or the Cone That Lost Its Head
  
  ##### Age 14 to 16Challenge Level
  
  How much peel does an apple have?
  
  ### Ball Packing
  
  ##### Age 14 to 16Challenge Level
  
  If a ball is rolled into the corner of a room how far is its centre from the corner?
  
  ### Volume of a Pyramid and a Cone
  
  ##### Age 11 to 14
  
  These formulae are often quoted, but rarely proved. In this article, we derive the formulae for the volumes of a square-based pyramid and a cone, using relatively simple mathematical concepts.
  
  ### Efficient Cutting
  
  ##### Age 11 to 14Challenge Level
  
  Use a single sheet of A4 paper and make a cylinder having the greatest possible volume. The cylinder must be closed off by a circle at each end.
  
  ### Mouhefanggai
  
  ##### Age 14 to 16
  
  Imagine two identical cylindrical pipes meeting at right angles and think about the shape of the space which belongs to both pipes. Early Chinese mathematicians call this shape the mouhefanggai.
  
  ### Which Solid?
  
  ##### Age 7 to 16Challenge Level
  
  This task develops spatial reasoning skills. By framing and asking questions a member of the team has to find out what mathematical object they have chosen.
  
  ### When the Angles of a Triangle Don't Add up to 180 Degrees
  
  ##### Age 14 to 18
  
  This article outlines the underlying axioms of spherical geometry giving a simple proof that the sum of the angles of a triangle on the surface of a unit sphere is equal to pi plus the area of the. . . .
  
  ### In a Spin
  
  ##### Age 14 to 16Challenge Level
  
  What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?
  
  ### Packing 3D Shapes
  
  ##### Age 14 to 16Challenge Level
  
  What 3D shapes occur in nature. How efficiently can you pack these shapes together?
  
  ### Fill Me up Too
  
  ##### Age 14 to 16Challenge Level
  
  In Fill Me Up we invited you to sketch graphs as vessels are filled with water. Can you work out the equations of the graphs?
  
  ### Three Balls
  
  ##### Age 14 to 16Challenge Level
  
  A circle has centre O and angle POR = angle QOR. Construct tangents at P and Q meeting at T. Draw a circle with diameter OT. Do P and Q lie inside, or on, or outside this circle?
  
  ### There and Back Again
  
  ##### Age 11 to 14Challenge Level
  
  Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?
  
  ### Immersion
  
  ##### Age 14 to 16Challenge Level
  
  Various solids are lowered into a beaker of water. How does the water level rise in each case?
  
  ### Paint Rollers for Frieze Patterns.
  
  ##### Age 11 to 16
  
  Proofs that there are only seven frieze patterns involve complicated group theory. The symmetries of a cylinder provide an easier approach.
  
  ### Gym Bag
  
  ##### Age 11 to 16Challenge Level
  
  Can Jo make a gym bag for her trainers from the piece of fabric she has?
  
  ### Make Your Own Pencil Case
  
  ##### Age 11 to 14Challenge Level
  
  What shape would fit your pens and pencils best? How can you make it?
  
  ### Witch's Hat
  
  ##### Age 11 to 16Challenge Level
  
  What shapes should Elly cut out to make a witch's hat? How can she make a taller hat?
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