Boxed In

A box has faces with areas 3, 12 and 25 square centimetres. What is the volume of the box?

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?

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?

Cuboids

Age 11 to 14 Challenge Level:

Find a cuboid (with edges of whole number lengths) that has a surface area of exactly $100$ square units.

Is there more than one?

Can you find them all?

Can you provide a convincing argument that you have found them all?