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Plutarch's Boxes

According to Plutarch, the Greeks found all the rectangles with integer sides, whose areas are equal to their perimeters. Can you find them? What rectangular boxes, with integer sides, have their surface areas equal to their volumes?

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Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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Sending a Parcel

What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?

Boxed In

Age 11 to 14 Challenge Level:

The diagram shows a rectangular box (a cuboid).
The areas of the faces are $3$, $12$ and $25$ square centimetres.
What is the volume of the box?

The areas of the faces of a cuboid are p, q and r. What is the volume of the cuboid in terms of p, q and r?