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Can you work out the dimensions of the three cubes?

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The builders have dug a hole in the ground to be filled with concrete for the foundations of our garage. How many cubic metres of ready-mix concrete should the builders order to fill this hole to make the concrete raft for the foundations?

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What is the volume of the solid formed by rotating this right angled triangle about the hypotenuse?

Funnel

Age 14 to 16
Challenge Level

As an example of how you might begin, take one litre as the volume.

How many cubic centimetres is that ?

If the radius was 1 cm, 2 cm, 3 cm, etc. what would the height be each time ?

And how long would the 'slope length' be in each case ?

How do you calculate the curved surface area using those things ?

When was the curved surface area least ?

Can you refine your answer with more precise values tried for the radius length ?

Could a spreadsheet help with the repeated calculation ?