Surface and surface area

There are 25 NRICH Mathematical resources connected to Surface and surface area
Changing areas, changing volumes
problem
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Changing areas, changing volumes

Age
11 to 14
Challenge level
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How can you change the surface area of a cuboid but keep its volume the same? How can you change the volume but keep the surface area the same?
Brush Loads
problem
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Brush loads

Age
7 to 11
Challenge level
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How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Cubes
problem
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Cubes

Age
7 to 11
Challenge level
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How many faces can you see when you arrange these three cubes in different ways?
Cola can
problem
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Cola can

Age
11 to 14
Challenge level
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An aluminium can contains 330 ml of cola. If the can's diameter is 6 cm what is the can's height?

Funnel
problem
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Funnel

Age
14 to 16
Challenge level
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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 ?
Three cubes
problem
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Three cubes

Age
14 to 16
Challenge level
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Can you work out the dimensions of the three cubes?
Painted Cube
problem
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Painted cube

Age
14 to 16
Challenge level
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Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?
The Spider and the Fly
problem
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The spider and the fly

Age
14 to 16
Challenge level
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A spider is sitting in the middle of one of the smallest walls in a room and a fly is resting beside the window. What is the shortest distance the spider would have to crawl to catch the fly?
Cuboids
problem
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Cuboids

Age
11 to 14
Challenge level
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Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?