Spheres, cylinders and cones

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Sponge Sections

Age

7 to 11

Challenge level

You have been given three shapes made out of sponge: a sphere, a cylinder and a cone. Your challenge is to find out how to cut them to make different shapes for printing.
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Which Solid?

Age

7 to 16

Challenge 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.
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Efficient Cutting

Age

11 to 14

Challenge 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.
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Cola Can

Age

11 to 14

Challenge level

An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?
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Immersion

Age

14 to 16

Challenge level

Various solids are lowered into a beaker of water. How does the water level rise in each case?
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Fill Me Up Too

Age

14 to 16

Challenge 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?
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Favourite

Funnel

Age

14 to 16

Challenge 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 ?
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Conical Bottle

Age

14 to 16

Challenge 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?
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Mesh

Age

16 to 18

Challenge level

A spherical balloon lies inside a wire frame. How much do you need to deflate it to remove it from the frame if it remains a sphere?
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There and Back Again

Age

11 to 14

Challenge level

Bilbo goes on an adventure, before arriving back home. Using the information given about his journey, can you work out where Bilbo lives?