Under the surface

What is the difference between surface area and volume of 3D shapes and solids? How are they calculated?

Image of a cubic metre constructed with straws.

Explore

How big a box can you make from a single piece of paper? This nrich.org problem is a classic optimisation question. On the other hand, sometimes you might be looking for the smallest box - this puzzle will get you thinking differently about volume and space.

Your tasks

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Investigate the difference between volume and surface area.

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Pose and solve a practical problem and contribute to other solutions.

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Use dynamic geometry software to break down surface area calculations and examine unit conversions.

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Examine the effect on volume and surface area of scaling up a solid in this task.

Syllabus links | Teaching notes (DOCX 68kB)